text:
Q: Possible to do xsl transform on dynamically generated xml? Let's say I have an empty XML file like so:
<root></root>

And I want to add an element to root during an XSL transformation like so:
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

  <xsl:output method="xml" encoding="UTF-8" omit-xml-declaration="yes" />

  <xsl:template match="@*|node()">
    <xsl:copy>
      <xsl:apply-templates select="@*|node()" />
    </xsl:copy>
  </xsl:template>

  <xsl:template match="/">
    <xsl:copy>
      <xsl:element name="root">
        <xsl:element name="label">Some text</xsl:element>
      </xsl:element>
    </xsl:copy>
  </xsl:template>

</xsl:stylesheet>

Transforming the XML file gives me:
<root>
  Some text
</root>

However, I'd like to modify the XSL file so that I can transform the runtime-generated XML. Basically, I'd like the XSL to think that the original XML file contained the dynamically created XML and then do an HTML transform on that.
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

  <xsl:output method="html" encoding="UTF-8" omit-xml-declaration="yes" />

  <xsl:template match="@*|node()">
    <xsl:copy>
      <xsl:apply-templates select="@*|node()" />
    </xsl:copy>
  </xsl:template>

  <xsl:template match="/">
    <xsl:copy>
      <xsl:element name="root">
        <xsl:element name="label">Some text</xsl:element>
      </xsl:element>
    </xsl:copy>
  </xsl:template>

  <xsl:template match="//label">

      <xsl:value-of select="." />

  </xsl:template>

</xsl:stylesheet>

In this case, my desired output would be: label.
Is it possible to do this in one XSL file? Am I looking at this problem incorrectly?

A: There are three essential elements to running a multi-pass transform.

*

*<xsl:import>

*<xsl:apply-imports>

*node-set() extension function

The example passes an XML document through two transforms serially. That is, it passes the content through a transform that removes namespace nodes and then takes the output from the first transform and passes it through a second transform that changes the title of the document. In this case the document is an XHTML document. The second transform is written such that it cannot accept an XHTML document with a namespace defined.
Original XHTML document
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

    <title>This is the old title</title>

This is some text.

After pass 1 (remove namespace nodes)

    <title>This is the old title</title>

This is some text.

Result (after pass 2)
Note that the title text has changed.

    <title>This is the new title</title>

This is some text.

XSLT for pass 1
This transform applies templates in this file to the content to remove namespace nodes, but copies the rest of the content. Then, during pass 2, applies the templates that are defined in the imported XSLT by using the <xsl:apply-imports> tag. The templates for pass 2 are imported using the <xsl:import> tag.
The results of the first pass are stored in a variable named "treefrag". The tree fragment is converted to a node-set using the extension function "node-set()". In this example, the Microsoft XML parser 4.0 is used, so the urn:schemas-microsoft-com:xslt namespace is declared.
<xsl:stylesheet version="1.0"
  xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
  xmlns:msxsl="urn:schemas-microsoft-com:xslt"
>

  <xsl:import href="pass2.xslt" />
  <xsl:output method="xml" version="1.0" encoding="UTF-8" indent="yes" />

  <xsl:template match="/">
    <xsl:param name="pass">1</xsl:param>

    <xsl:choose>
      <xsl:when test="$pass=1">
        <xsl:variable name="treefrag">
          <xsl:apply-templates>
            <xsl:with-param name="pass" select="$pass" />
          </xsl:apply-templates>
        </xsl:variable>
        <xsl:variable name="doc" select="
          msxsl:node-set($treefrag)
        " />
        <xsl:apply-templates select="$doc">
          <xsl:with-param name="pass">2</xsl:with-param>
        </xsl:apply-templates>
      </xsl:when>
      <xsl:when test="$pass=2">
        <xsl:apply-imports />
      </xsl:when>
    </xsl:choose>

  </xsl:template>

  <xsl:template match="*">
    <xsl:param name="pass">2</xsl:param>

    <xsl:choose>
      <xsl:when test="$pass=1">
        <xsl:element name="{name()}">
          <xsl:apply-templates select="@*|node()">
            <xsl:with-param name="pass" select="$pass" />
          </xsl:apply-templates>
        </xsl:element>
      </xsl:when>
      <xsl:when test="$pass=2">
        <xsl:apply-imports />
      </xsl:when>
    </xsl:choose>
  </xsl:template>

  <xsl:template match="@*|text()|comment()|processing-instruction()">
    <xsl:param name="pass">2</xsl:param>

    <xsl:choose>
      <xsl:when test="$pass=1">
        <xsl:copy>
          <xsl:apply-templates select="@*|node()">
            <xsl:with-param name="pass" select="$pass" />
          </xsl:apply-templates>
        </xsl:copy>
      </xsl:when>
      <xsl:when test="$pass=2">
        <xsl:apply-imports />
      </xsl:when>
    </xsl:choose>
  </xsl:template>
</xsl:stylesheet>

XSLT for pass 2
This transform simply changes the contents of the TITLE tag can copies all the rest of the content.
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

  <xsl:output method="xml" version="1.0" encoding="UTF-8" indent="yes"/>

  <xsl:template match="title">
    <title>This is the new title</title>
  </xsl:template>

  <xsl:template match="@*|node()">
    <xsl:copy>
      <xsl:apply-templates select="@*|node()"/>
    </xsl:copy>
  </xsl:template>

</xsl:stylesheet>

Source article: "XSLT: Multi-pass transforms"

A: Doug's answer is technically correct, and he put me on the right path of looking for the nodeset extension function (thanks!).  The only difference is that I'm using the Xalan-java processor instead of the microsoft one.  Here is a working (extremely simple) example of what I was trying to achive:
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
            xmlns:xalan="http://xml.apache.org/xalan" exclude-result-prefixes="xalan">
<xsl:output method="html" encoding="UTF-8" omit-xml-declaration="yes"/>

<xsl:template match="label">
    <xsl:value-of select="." />
</xsl:template>

<xsl:template name="someTemplate">
    <root>
        hey there
    </root>
</xsl:template>

<xsl:template match="/">
    <xsl:variable name="gen">
        <xsl:call-template name="someTemplate" />
    </xsl:variable>

    <xsl:apply-templates select="xalan:nodeset($gen)//label" />
</xsl:template>

</xsl:stylesheet>

The basic idea is that you create a variable (here named "gen") that calls a template ("someTemplate") which creates some xml.  That xml tree is then processed by the xalan:nodeset function.  Here, I run apply-templates and process all label fields, which matches with my label template and creates the bolded label.
The reason why I'm doing all this is because I'm working on a web-app where all the content on each page is defined in XML and then processed using XSL.  This works great until you want to fill parts of the page with the results of an AJAX call, because then you either need to build the new html inside a javascript function from the returned XML (messy and bad) or pass the AJAX XML response through an XSL transform on the server side and just insert the xhtml result into the page.
In my situation, because I'm describing each web page in XML, I've created simple, generic elements that have "types".  My elements are "block", which is any block of content.  A block can have sub-nodes such as "button" (Which is a link or button), "list" (which is multiple blocks), "image", or "input".  The details of the schema are irrelevant; I just wanted to show that my XML schema is very simple and generic.
On the other hand, the AJAX XML response that I'm retrieving to refresh/build up the page is being created by a third-party that does not use my schema.  On the contrary, each service they provide returns very specific XML for each unique request.  For this reason, I need a way to convert their very specific XML into my very generic XML so that I can transform it using a single set of XSL templates.
Here is a sample of one of the xsl templates I'm now using that transforms the AJAX response and converts their specific XML to my generic XML.
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
            xmlns:xalan="http://xml.apache.org/xalan" exclude-result-prefixes="xalan">
<xsl:output method="html" encoding="UTF-8" omit-xml-declaration="yes"/>

<xsl:include href="base.xsl" />

<xsl:template name="templateForAJAXResponse">
    <block>
        <type>list</type>
        <list>
            <type>itemBrowser</type>
            <xsl:for-each select="/response/items/item">
                <block>
                    <type>button</type>
                    <button>
                        <type>imageButton</type>
                        <href>something.action</href>
                        <src><xsl:value-of select="src" /></src>
                        <title><xsl:value-of select="name" /></title>
                    </button>
                </block>
            </xsl:for-each>
        </list>
    </block>
</xsl:template>

<xsl:template match="/">
    <xsl:variable name="gen">
        <xsl:call-template name="templateForAJAXResponse" />
    </xsl:variable>

        <xsl:apply-templates select="xalan:nodeset($gen)/block" />

</xsl:template>

</xsl:stylesheet>

redpajama_set_name: RedPajamaStackExchange


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I started this recipe as I do most of my cooking with a baseline of a recipe and then improvise. I was looking for a cheddar cheese soup recipe online that I could actually make. Many had carrots, onions, chicken, broths, and various other things that I couldn't eat myself and I'm sure make super soup, but if you can't eat it then it's not really good is it?
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**This is an excellent recipe for busy Mom's with kids who need to put on weight as it's easy to alter to your child's tastebuds and easy to make in a hurry and take with you.


text:
\section{Introduction}
Recently, there has been a renewed interest in the search of a
modified theory of gravity at large distances through a massive
deformation of GR  (see for a recent review ~\cite{Hint}). A great
deal of effort was devoted  to extend at the
nonlinear level~\cite{Gabadadze:2010} the seminal work of
Fierz and Pauli (FP)~\cite{Fierz:1939ix}.  The FP theory is defined at linearized level and is
plagued by a number of diseases. In particular, the modification of
the Newtonian potential is not continuous when the mass $m^2$
vanishes, giving a large correction (25\%) to the light deflection
from the sun that is experimentally excluded~\cite{DIS}. A possible
way to circumvent the the discontinuity problem is to suppose
that~\cite{Vainshtein} the linearized
approximation breaks down near a massive object like the sun and an improved perturbative
expansion.
In addition, FP is problematic as an effective theory. Regarding FP as
a gauge theory where the gauge symmetry is broken by a explicit mass
term $m$, one would expect a cutoff $\Lambda_2 \sim m g^{-1} = (m
M_{pl})^{1/2}$, however the real cutoff is $\Lambda_5 = (m^4
M_{pl})^{1/5}$ or $\Lambda_3 = (m^2 M_{pl})^{1/3}$, much
lower than $\Lambda_2$ \cite{AGS}. A would-be Goldstone mode is responsible for
the extreme $UV$ sensitivity of the FP theory, that becomes totally
unreliable in the absence of proper UV completion.
Recently it was shown that there exists a non linear completion of the FP
theory~\cite{Gabadadze:2011} that is free of ghosts up to the fourth
order \cite{Gabadadze:2011}, avoiding the presence of the Boulware-Deser
instability~\cite{BD}.  Then the propagation of only five degrees of freedom (DoF)
was generalized to all orders in~\cite{GF}; this was shown also in the Stuckelberg language
in~\cite{deRham:2011qq}.

Quite naturally massive gravity leads to bigravity.  Indeed, any
massive deformation, obtained by adding to the Einstein-Hilbert
action a non-derivative self-coupling for the metric $g$, requires the
introduction of an additional metric $\tilde g$ that may be a fixed
external field, or be a dynamical one.
When $\tilde g$ is non-dynamical we are in the framework  of
\ae ther-like theories; on the
other hand if it is dynamical we enter in the realm of
bigravity~\cite{DAM1} that was originally introduced by Isham, Salam
and Strathdee~\cite{Isham}.  The need for a second
dynamical metric also follows from rather general grounds. Indeed, it
was shown in~\cite{DeJac} that in the case of non singular static
spherically symmetric geometry with the additional property that
the two metrics are diagonal in the same coordinate patch, a Killing
horizon for $g$ must also be a Killing horizon for $\tilde
g$; see~\cite{gabBH} for a concrete example. Actually it turns out that the off diagonal solutions show no
modification of gravity at large distance~\cite{us,ussphe}.
Also cosmology calls for the bigravity formulation of massive
gravity. When the second metric is static
there is no homogeneous spatially flat FRW solution~\cite{FRWfroz,Alberte,cur},
on the contrary  in the bigravity formulation flat FRW homogeneous solutions do
exist~\cite{uscosm,hasscosm,russ}. See also~\cite{Koy-cosm} for a
different approach to cosmology in massive gravity.
In this paper we study perturbations around the FRW background
solutions found in~\cite{uscosm}.

The outline of the paper is the following.
After a brief introduction to the bigravity formulation of massive
gravity in section~\ref{bi}, the FRW solutions are reviewed in section~\ref{frwsec}.
The perturbed FRW geometry is introduced in section~\ref{pert}  and the perturbed Einstein equations are given in
section~\ref{modeq}.  The dynamics of the perturbations in various
cases are studied in sections \ref{br1}, \ref{ds} and
\ref{br2}. Section~\ref{con} contains our conclusions.

\section{Massive Gravity and Bigravity}
\label{bi}
Any modification of GR that turns a massless graviton into a massive
one calls for additional DoF. An elegant way to provide them is to
work with an extra tensor $\tilde g_{\mu \nu}$. When coupled to the
standard metric $g_{\mu \nu}$, it allows to build non-trivial
diff-invariant operators that lead to mass terms  when expanded around
a background.  Consider the action
\begin{equation}
S=
\int d^4 x \left\{ \sqrt{\tilde g} \,   \kappa   \, M_{pl}^2\; \tilde {\cal R}+\sqrt{g} \;\left[
M_{pl}^2 \;\left( {\cal R}
-2 \, m^2   \, V \right)  + L_{\text{matt}} \right] \right\},
\label{act}
\end{equation}
where $R(g_i)$ are the corresponding Ricci scalars and the interaction
potential $V$ is a scalar function of the tensor $X^\mu_\nu = {g}^{\mu
\alpha} {\tilde g}_{\alpha \nu}$.  Matter is minimally coupled to
$g$ and it is described by $L_{matt}$. The constant $\kappa$ controls
the relative size of the strength of gravitational interactions in the
two sectors, while $m$ sets the scale of the graviton mass. The action
(\ref{act}) brings us into the realm of bigravity theories, whose
study started in the '60 (see \cite{DAM1} for early references).  An
action of the form (\ref{act}) can be also viewed as the effective
theories for the low lying Kaluza-Klein modes in brane world
models~\cite{DAM1}. The massive
deformation is encoded in the non derivative coupling between
$g_{\mu\nu}$ and the extra tensor field $\tilde g_{\mu \nu}$. Clearly
the action is invariant under diffeomorphisms, which transform the two
fields in the same way (diagonal diffs).
Taking the limit $\kappa \to \infty$, the
second metric decouples, and gets effectively frozen to a fixed
background value so that the ``relative'' diffeomorphisms are
effectively broken, as far as the first metric is concerned.
Depending on the background value of $\tilde g_{\mu \nu}$ one can
explore both the Lorentz-invariant (LI) and the Lorentz-breaking (LB) phases of
massive gravity~\cite{PRLus} \cite{blasmy}. When the second metric is dynamical this is
determined by its asymptotic properties, as discussed below. In this
case notice that $\tilde g_{\mu \nu}$ is determined by its equations
of motion (for any finite $\tilde M_{pl}$) so that we will be working
always with consistent and dynamically determined backgrounds.  The
role played by $\tilde g_{\mu \nu}$ is very similar to the Higgs
field, its dynamical part restores gauge invariance and its background
value determines the realization of the residual symmetries.

The modified Einstein equations can be written as\footnote{When not
specified, indices of tensors related with $g$($\tilde g$) are raised/lowered with
$g(\tilde g)$}
\begin{gather}
\label{eqm1}
\,{E}^\mu_\nu  +  Q_1{}^\m_\n = \frac{1}{2\;M_{pl}^2 }\, {T}^\mu_\nu   \\
\label{eqm2}
\kappa  \, {\tilde E}^\mu_\nu  +  Q_2{}^\m_\n = 0 \; ;
\end{gather}
where we have defined $Q_1$ and $Q_2$ as effective energy-momentum tensors induced by the
interaction term. The only invariant tensor that can be written without derivatives out
of $g$ and $\tilde g$ is $X^\mu_\nu = g^{\mu \alpha}_1 {\tilde g}_{\alpha
\nu}$ \cite{DAM1}. The ghost free
potential~\cite{Gabadadze:2011}\footnote{A very similar potential
  having the same form but with $X$ instead of $X^{1/2}$ was
  considered in~\cite{us}.}  $V$ is  a special  scalar function
of $Y^\mu_\nu=(\sqrt{X})^\mu_\nu$ given by
\begin{equation}
\label{eq:genpot}
\qquad V=\sum_{n=0}^4 \, a_n\, V_n \,,\qquad n=0\ldots4 \, ,
\end{equation}
where The $V_n$ are the symmetric polynomials of $Y$
\begin{equation}
\begin{split}
&V_0=1\,\qquad
V_1=\tau_1\,,\qquad
V_2=\tau_1^2-\tau_2\,,\qquad
V_3=\tau_1^3-3\,\tau_1\,\tau_2+2\,\tau_3\,,\\[1ex]
&V_4=\tau_1^4-6\,\tau_1^2\,\tau_2+8\,\tau_1\,\tau_3+3\,\tau_2^2-6\, \tau_4\,,
\end{split}
\end{equation}
with $\tau_n=\tr(Y^n)$.  In \cite{HRBI} it was shown that in the bimetric
formulation the potential $V$ is ghost free. We have that
\begin{eqnarray}
\label{eq:q1}
 Q_1{}_\nu^\mu &=&  { m^2}\, \left[ \;  V\; \delta^\mu_\nu \,  - \,  (V'\;Y)^\mu_\nu  \right]\\[1ex]
\label{eq:q2}
 Q_2{}_\nu^\mu &=&  m^2\, q^{-1/2} \, \; (V'\;Y)^\mu_\nu ,
\end{eqnarray}
where  $(V^\prime)^\mu_\nu = \partial V / \partial Y_\mu^\nu$ and  $q =\det
X=\det(\tilde g)/\det(g)$.

The canonical analysis~\cite{GF} shows that in general 7 DoF propagate; around a
Minkowski background, 5 can be associated to a massive spin two
graviton and the remaining 2 to a massless spin two graviton.

\section{FRW Solutions in Massive Gravity}
\label{frwsec}
Let us review the FRW background solutions in massive gravity~\cite{uscosm} that are of the form
\begin{equation}
\begin{split}
ds^2 &=   a^2(\tau) \left(- d \tau^2 +   dr^2 + r^2 \, d \Omega^2 \right) =
 {\bar g}_{1 \, \mu \nu} dx^\mu dx^\nu\\
\tilde{ds}^2 &= \omega^2(\tau) \left[- c^2(\tau) \, d \tau^2 + dr^2+  r^2 \, d
  \Omega^2 \right] =
 {\bar g}_{2 \, \mu \nu} dx^\mu dx^\nu\, .
\label{frw}
\end{split}
\end{equation}
It is convenient to define the  standard Hubble
parameters for the two metrics
\begin{equation}
{\cal H} =\frac{d a}{d\tau}  \frac{1}{a} \equiv \frac{a'}{a}= H \, a  \, ,
\qquad {\cal H}_\o = \frac{\o'}{\o} = H_\o \, \o \, , \qquad \xi =
\frac{\o}{a} \, .
\end{equation}
Solutions fall in two branches depending on how the Bianchi
identities are realized.
\begin{itemize}
\item
In branch one, $\xi=\bar \xi$ is constant and satisfies the following algebraic equation
\begin{equation}
f_2(\bar \xi) =0 \, \qquad \text{with } f_2(\xi)= 6\, a_3 \, \xi^2+4\, a_2 \, \xi +a_1  .
\label{cb1}
\end{equation}
As a consequence, the Hubble parameter ${\cal H}$ of $g$ and
the one of $\tilde g$, ${\cal H}_\o$ coincide and
\begin{equation}
\frac{{\cal H}^2}{a^2} =\frac{8 \pi G}{3}  \left( \rho  +
  \Lambda_{1} \right) \, , \qquad \Lambda_{1} =\frac{ m^2 }{ 8 \pi G}  \left[ a_0-6 \,{\bar \xi}^2\,
  \left(2\, a_3 \,\bar \xi +a_2 \,\right)\right] \; .
\label{tteq}
\end{equation}
In this branch the effect of the mass deformation is to induce an
effective cosmological constant and
\begin{equation}
c =\sqrt{\frac{\Lambda_{1}+\rho }{\Lambda_2}}\qquad {\rm with}\quad  \Lambda_{2} =\frac{ m^2 }{ 4 \pi G\,\kappa}   \left[6\, \bar \xi\,  \left(2\, a_4 \,\bar \xi
   +a_3 \, \right)+a_2\right]  \, .
\end{equation}
This is not very surprising,
indeed, the constraint (\ref{cb1}),  in the spherically symmetric case,
leads  to a branch of solutions with no modification of gravity,
being the graviton mass zero around a flat background~\cite{ussphe}.
\item
In branch two, $\xi$ is not constant and  the Bianchi identities are realized in the form
\begin{equation}
c = \frac{H_\o}{H} \, \xi =  \frac{{\cal H}_\o}{{\cal H}} ,\;\;\;\;\;\; \xi'=(c-1)\;{\cal H}\;\xi
\;\;\;\;  {\rm with}\;\;\; c>0 \, ,
\label{bnew}
\end{equation}
and
\begin{equation}
\frac{3 \mathcal{H}^2}{a^2}= 8 \pi  G \, \rho  + m^2 \left(6 a_3 \,
  \xi ^3+6 a_2 \,  \xi^2+3 a_1 \,  \xi +a_0 \right) \, .
\end{equation}
The ratio $\xi$ of the two scale parameters satisfies the equation
\b
 &&m^2 \left[\xi ^2 \left(\frac{8\; a_4}{\kappa }-2\; a_2\right)+\xi
   \left(\frac{6 \; a_3}{\kappa }-a_1\right)+\frac{a_1}{3 \; \kappa \,
   \xi }+\frac{2 \; a_2}{\kappa }-2\;  a_3 \, \xi ^3-\frac{a_0}{3}\right]

=\frac{8 \pi  G \; \rho  }{3}  \, .
\label{conII}
\end{eqnarray}
\end{itemize}
In the expanding universe, the ratio $\frac{8 \pi  G \; \rho  }{m^2}$
scales rapidly with redshift $z$, $1+z\equiv
a(\tau_{today})/a(\tau)$. Indeed,
assuming that the mass scale $m$ is related to the present
cosmological constant as $\; m^2\,M_{pl}^2\propto \Lambda$ and that
for matter with an equation of state $p  = w \, \rho $,  $\rho  =
\rho_0 \, (1+z)^{3(w+1)}$, we have
\begin{equation}
\frac{8 \pi  G \; \rho  }{m^2}\sim \frac{\Omega_m}{\Omega_{\Lambda}}
\;z^{3(w+1)}\gg 1 \quad {\rm at\; early\; times.}
\end{equation}
This quantity gets very large already at redshift $z\sim 10$,
much later than the radiation era ($z\sim 10^4$).
Thus, eq.(\ref{conII}) can be satisfied only in two regimes:
for  large or   small values of $\xi$~\footnote{In presence of
  ``mirror'' matter with energy density $\tilde \rho$ minimally
  coupled with the  second metric $\tilde g$,  eq.(\ref{conII}) gets
  modified as $\rho \to \rho  -\xi^2\,\tilde\rho /\kappa$ and
the small-large $\xi$ regime solutions can be evaded as soon as $\xi^2\sim \kappa\,\rho/ \tilde \rho$, when $m \to 0$.}.
The large $\xi$ regime is physically uninteresting because $c<0$ when
matter has $w>0$ \cite{uscosm}.
In the small   $\xi$  regime,  cosmology is very similar to the standard one;
for  $a_1> 0$ we have
\begin{eqnarray}
\xi &=&\frac{a_1\; m^2}{8\,\pi\, G \, \kappa\,\rho } + {\cal O}\left({\frac{m^2}{G\,\rho }}\right)^2 \sim z^{-3(w+1)}\; \, ;\\
&&\rho  +\rho_g =  \rho \left(1+{\cal O}\left(\frac{m^2}{G\,\rho }\right)\right) \, ;\\
 && w_{eff} = w +{\cal O}\left(\frac{m^2}{G\,\rho }\right) \, ,
 \quad \qquad c=(4+3\,w)+{\cal O}\left(\frac{m^2}{G\,\rho }\right) \, .
\end{eqnarray}
Once the matter is so diluted that $\rho $ is negligible in
(\ref{conII}) the system falls in the fixed point region and $\xi$ is
almost constant and the universe  enters in a late time
dS phase.
The analysis  is identical when the {\it same}  spatial
curvature $k_c$ is introduced in (\ref{frw})\footnote{The spatial
curvatures must be equal for consistency~\cite{uscosm}.} for both metrics.

Let us now discuss the
differences with the frozen metric approach where
 $\tilde g$ is non dynamical.  Formally, the
non-dynamical limit corresponds to $\kappa \to \infty$.
To make contact with the existing literature, we take $\tilde g$ equivalent
to the Minkowski flat metric implying clearly that $c$ and $\omega$
cannot be arbitrary. Indeed, imposing that the Riemann curvature
tensor of   $\tilde g$ vanishes we get that $k_c <0 $ and
\begin{equation}
c= \frac{{\cal H}_\o}{\sqrt{-k_c}} \, .
\label{cflat}
\end{equation}
Thus, flat  FRW cosmology with frozen second metric exists only with a negative
non-vanishing spatial curvature~\cite{FRWfroz}-\cite{uscosm}. When
(\ref{cflat}) holds, Bianchi identities can be realized only within
branch one, leading to eq.(\ref{cb1}).
 That is why FRW perturbations in the Stuckelberg formalism are stuck  into  branch one that is rather problematic.

\section{Perturbed FRW Geometry}
\label{pert}
Let us now consider the perturbations of the FRW background (\ref{frwsec})
\begin{equation}
g_{\mu \nu} = \,  \bar g_{1 \, \mu \nu}  +a^2 \,  {h_1}_{\mu
  \nu} \, , \qquad {\tilde g}_{\mu \nu} =  \bar g_{2 \, \mu \nu}  +
 \o^2 \,  h_{2 \, \mu \nu}  \, .
\end{equation}
parametrized as follows
\begin{equation}
\begin{split}
& {h}_{1 \, 00} \equiv - 2 A_1  \, , \qquad  {h}_{2 \, 00}  \equiv - 2 c^2 \, A_2\\
& {h}_{1/2 \, 0 i}  \equiv {\cal C}_{1/2 \,i} - \partial_i B_{1/2}  \, , \qquad
\partial^i {\cal V}_{1/2 \, i}=  \partial^i {\cal C}_{1/2 \, i} = \partial^j {h^{TT}}_{1/2 \, ij} =
\delta^{ij} {h^{TT}}_{1/2 \, ij}  =0  \, ,\\
& h_{1/2 \, ij}  \equiv {h^{TT}}_{1/2 \, ij} + \partial_i {\cal V}_{1/2 \, j} + \partial_j {\cal
  V}_{1/2\, i} + 2 \partial_i \partial_j E_{1/2} + 2 \, \delta_{ij} \, F_{1/2}  \,.
\end{split}
\end{equation}
Spatial indices are raised/lowered using the spatial flat metric.

Under a gauge transformation generated by $\zeta^\mu$ the metric perturbation transforms
\begin{equation}
\begin{split}
& \delta h_{1 \, \mu \nu } = a^{-2} \left(\zeta^\alpha \partial_\alpha  {\bar g}_{1 \,
  \mu \nu} +  \bar g_{1 \, \alpha \nu}  \, \partial_\mu
  \zeta^\alpha + \bar g_{1 \, \mu \alpha}  \, \partial_\nu \zeta^\alpha \right)
\, , \\[.2cm]
&\delta h_{2 \, \mu \nu } = \o^{-2} \left(\zeta^\alpha \partial_\alpha \, {\bar
  g}_{2 \,\mu \nu } +  \bar g_{2 \, \alpha \nu}  \, \partial_\mu
  \zeta^\alpha + \bar g_{2 \, \mu \alpha}  \, \partial_\nu \zeta^\alpha \right) \, .
\end{split}
\end{equation}
and for the corresponding components
\begin{equation}
\begin{split}
&\delta A_1 = {\cal H} \, \zeta^0 + {\zeta^0}^\prime \, ,
\quad \delta B_1 =
\zeta^0 -\zeta^\prime \, , \quad \delta E_1 =  \zeta \, ,  \quad
\delta F_1 =  {\cal H} \, \zeta^0
\, ; \\
&\delta A_2 = {\cal H}_\beta \, \zeta^0 + {\zeta^0}^\prime \, ,
\quad \delta B_2 =
 c^2 \, \zeta^0 - \zeta^\prime \, , \quad \delta E_2 =  \zeta \, ,  \quad \delta F_2 =  {\cal H}_\o \zeta^0
\, ; \\
& \delta {\cal C}_{1/2 \, i} = {\zeta^i_T}' \, , \quad \delta {\cal
  V}_{1/2 \, i} =  {\zeta^i_T} \,  , \qquad \delta {h^{TT}}_{1/2 \, ij}  =0 \, ; \\
\end{split}
\label{gtr}
\end{equation}
where
\begin{equation}
\begin{split}
&\zeta^i = \zeta^i_T + \partial_i
\zeta \, , \qquad\zeta = \Delta^{-1} \partial_i \zeta^i \, ,  \\[.2cm]
& {\cal H}_\beta=\frac{ (c
  \, \omega)'}{(c \, \o)} =\frac{c'}{c} +\o \, {\cal H}_\o \, .
\end{split}
\end{equation}
In the scalar sector we have 8 fields and two independent gauge
transformations, as a result we can form 6 independent gauge invariant
scalar combinations  that we chose to be
\begin{equation}
\begin{split}
& \Psi_1= A_1 - {\cal H} \, \Xi_1   - \Xi_1^\prime \qquad \Psi_2= A_2 + c^{-2} \left(\frac{c'}{c} - {\cal H}_\o \right) \, \Xi_2   -
\frac{\Xi_2^\prime}{c^2}  \\
&\Phi_1 = F_1- {\cal H} \, \Xi_1 \, , \qquad \Phi_2 = F_2 - {\cal
  H}_\o \, \frac{\Xi_2}{c^2}  \, , \\
&{\cal E} = E_1 - E_2 \, ,  \qquad {\cal B}_1 = B_2 - c^2
B_1 +(1-c^2) \, E_1' \, ,
\end{split}
\label{sgib}
\end{equation}
where $\Xi_{1/2} = B_{1/2} + E_{1/2}^\prime$. The following additional
gauge invariant fields will be useful to write in a compact form the
perturbed Einstein equations
\begin{equation}
\begin{split}
&{\cal F}_1=F_2-F_1 +\left({\cal H} - {\cal  H}_\o \right) \Xi_1 \, ,
\qquad {\cal F}_2=F_2-F_1 +\left({\cal H} -
{\cal  H}_\o \right) \frac{\Xi_2}{c^2} \, , \\
 &{\cal B}_2 = B_2 - c^2 B_1 +(1-c^2) \, E_2' \, , \\
&{\cal A}_1 = c (A_2-A_1) + \left[c \left({\cal H} -
{\cal  H}_\o \right) - c'\right] \Xi_1 \, , \\
& {\cal A}_2 = c
(A_2-A_1) + \left[c \left({\cal H} -
{\cal  H}_\o \right) - c'\right] \frac{\Xi_2}{c^2} \, .
\end{split}
\end{equation}
The fields ${\cal F}_{1/2}$, ${\cal A}_{1/2}$ and ${\cal B}_2$ can be
expressed in terms of the ones in (\ref{sgib}), as it is shown in
Appendix~\ref{rel}.  In the matter sector, we define the following gauge
invariant perturbed pressure and density
\begin{equation}
\delta \rho_{gi} = \delta \rho - \Xi_1 \, \rho' \, , \qquad \delta
p_{gi} = \delta p - \Xi_1 \, p'
 \, .
\end{equation}
For matter, together with pressure and density perturbation, there is
also the perturbed 4-velocity $u^\mu$ that consists of a scalar part
$v$ and a vector part $\delta z_i$
\begin{equation}
\begin{split}
&u^\mu = {\bar u}^\mu  + \delta u^\mu \, , \qquad u^\mu u^\nu g_{\mu
  \nu} = -1 \, , \quad \delta u^0 = - a^{-1} \,  A_1 \, ;  \\
& \delta u_i = a \left( \partial_i v - \partial_i B_1 +  \delta z_i + {\cal
    C}_{1 i} \right) \, .
\end{split}
\end{equation}
The corresponding gauge invariant quantity are defined as
\begin{equation}
u_s = v + E_1' \, , \qquad {\delta v}_{ i} = \delta z_i + {\cal
  C}_{1 \, i} \, .
\end{equation}
The conservation of the matter EMT  leads to a set of differential
relations; for scalar matter perturbations we have
\begin{eqnarray}
\delta \rho_{gi}'=(1+w) \left[\rho \,\left( k^2 \, u_s-3 \, \Phi_1'
  \right) - 3  \, {\cal H } \, \delta \rho \right] \, ;\\
u_s'= (3 w-1) \, u_s \, {\cal H} - \frac{w}{(1+w)} \, \frac{\delta
\rho_{gi}}{\rho} - \Psi_ 1\, ;
\end{eqnarray}
while for vector matter perturbations
\begin{equation}
\delta v_i ' =\delta v_i \, (3 \,w-1)\,
   \mathcal{H} \, .
\label{vecc}
\end{equation}
In the vector sector we have 4 fields and 1 gauge transformation; thus,
we can form 3 independent gauge invariant vector perturbations
\begin{equation}
\begin{split}
& V_{1/2 \, i} = {\cal C}_{1/2 \, i} - {\cal V}_{1/2 \, i}^\prime \, ,
\quad \chi_i = {\cal C}_{1 \, i}-  {\cal C}_{2 \, i} \, .
\end{split}
\end{equation}
\section{Perturbed Einstein Equations}
\label{modeq}
Let us start with the scalar sector.  The  leading order  perturbed Einstein equations for $g$ are
\begin{eqnarray}
&&2 \Delta  \Phi_1+6 {\cal H} \left(\Psi _1 \mathcal{H}-\Phi
  _1'\right) +a^2 m^2 \,  f_2 (3 {\cal F}_1-\Delta   {\cal
  E})  =-8 \pi  a^2 \,G \,\delta \rho_{\text{gi}} \, ; \label{1tt}\\[.3cm]
&&\partial_i \left[2 \Psi _1 \mathcal{H}-2 \Phi _1' +\frac{a^2 m^2  \,
    \mathcal{B}_1 \, f_2 }{(c+1)} +  8 \pi\,  G \,a^2\, (p+\rho )\,  u_s\right]
=0 \, ;  \label{1ts}\\[.3cm]
&&  \left(\partial_i \partial_j - \delta_{ij} \Delta \right)
   \left( a^2 \,f_1\, m^2 \mathcal{E} - \Phi_1- \Psi_1\right)  + \delta_{ij}
   \left[m^2   \, a^2 \,(2\, f_1\, \mathcal{F}_1  +f_2\, \mathcal{A}_1 )+2
     \Psi_1 \,\left(\mathcal{H}^2+2 \,\mathcal{H}'\right) \right. \nonumber \label{1ss}\\[.2cm]
&&\left. -2 \,\Phi_1''-2\, \mathcal{H} \left(2\, \Phi _1'-\Psi _1'\right)\right]
= 8 \pi  G \, a^2 \, \delta_{ij} \,
\delta p_{\text{gi}} \, ,
\end{eqnarray}
where
\begin{equation}
f_1 =\xi \, \left[2 \,\xi  \,\left(3\, a_3 \, c \, \xi +a_2
 \,  (c+1)\right)+a_1\right] \, , \qquad f_2 =\xi \, \left(6 \,a_3 \,\xi ^2+4
\, a_2\, \xi +a_1\right) \, .
\end{equation}
For the metric $\tilde g$ we have
\begin{eqnarray}
&&
2\,c^2 \Delta  \Phi _2+6
   \mathcal{H}_{\omega } \left(\Psi _2   \mathcal{H}_{\omega }-\Phi _2'\right)  +\frac{m^2  a^2  f_2}{\kappa\,\xi^2}\, c^2
\,   \left(\Delta  \mathcal{E}-3 \,\mathcal{F}_2\right)=0 \, ; \label{2tt}\\[.3cm]
&& \partial_i \left[ 2\, c \,
   \left(\Psi _2 \mathcal{H}_{\omega }-\Phi _2'\right)-\frac{m^2  \, a^2 \, f_2}{\kappa\,\xi^2\,(1+c)} \, \mathcal{B}_2\right] =0 \, ;
 \label{2ts}\\[.3cm]
&&
-c \, \left(\partial_i \partial_j - \delta_{ij} \Delta \right) \left[
\frac{a^2 \, f_1 \, m^2}{\kappa\,\xi^2} \, \mathcal{E}+ \, c   \, \left(\Phi_2+\Psi
     _2\right)\right]+\delta_{ij}\left[ \frac{m^2 \,a^2}{\kappa\,\xi^2} (2\,  c\, f_1 \, \mathcal{F}_2+  f_2 \, \mathcal{A}_2 ) +\right.
\nonumber\\[.2cm]
&&
\left.
2\left( \mathcal{H}_{\omega }^2+2\,\mathcal{H}_{\omega }'-2\,\frac{c'}{c}\, \mathcal{H}_{\omega }\right) \Psi _2-
2 \Phi_2''+2\left(\frac{c'}{c}-2\,\mathcal{H}_{\omega }\right)\, \Phi
_2'+2\,\mathcal{H}_{\omega }\,\Psi _2' \right]=0 \, . \label{2ss}
\end{eqnarray}
For the vector sector the perturbed Einstein equations are
\begin{eqnarray}
&& \frac{\Delta V_{1 \, i}}{2 \, a^2} - 8 \pi G  \, (\rho + p)  \, \delta v_i -
\frac{m^2 }{(1+c)} \, f_2 \, \chi_i =0 \, ; \label{1vts}\\[.3cm]
&&\partial_{(i} V_{1 \, j)}'  + 2 \,{\cal H}\,   \partial_{(i} V_{1 \, j)}
=m^2 \, a^2\, f_1\, \partial_{(i}
  {\cal V}_{12 \, j)}   \,
; \label{1vss} \\[.3cm]
&& \frac{\Delta V_{2 \, i}}{2 \,a^2 \, c } + \frac{ m^2 \, f_2 }{(1+c)\,\kappa\, \xi^2}  \, \chi_i =0 \, ; \label{2vts}\\[.3cm]
&&
\partial_{(i} V_{2 \, j)}' +  \left[2 \left( {\cal H }  +\, \frac{\xi '}{\xi} \right)-\frac{ c'}{ c}\right] \,
  \partial_{(i} V_{2 \, j)}
+ \, \frac{m^2\,a^2\, c  \, f_1}{\kappa\,\xi^2}\,   \partial_{(i}
{\cal V}_{12 \, j)} =0 \label{2vss} \, ;
\end{eqnarray}
where
\begin{equation}
{\cal V}_{12 \, i } ={\cal V}_{1\, i} -{\cal V}_{2 \, i } \, , \qquad
{V}_{12 \, i} ={ V}_{1\, i} -{V}_{2 \, i} \, .
\end{equation}
Notice that ${V}_{12 \,i} = \chi_i -{\cal V}_{12 \, i }' $.

Finally, for the tensor perturbations we obtain
\begin{eqnarray}
&&{h^{TT}}_{1 \, ij}'' + 2 {\cal H} \, {h^{TT}}_{1 \, ij}' - \Delta {h^{TT}}_{1 \, ij} + m^2  \, a^2 \,
f_1 \, \left(h^{TT}_{1 \, ij} -h^{TT}_{2 \, ij} \right) =0 \,
; \label{1t} \\[.3cm]
 && {h^{TT}}_{2 \, ij}'' +\left[2 \left(  {\cal H} +\frac{ \xi'}{\xi} \right)
 -   \,\frac{ c'}{c} \right] {h^{TT}}_{2 \, ij}'  - c^2   \, \Delta {h^{TT}}_{2 \, ij}
 - \frac{m^2 \,f_1 \, c }{ \kappa\, \xi^2} \, a^2  \,
   \left(h^{TT}_{1 \, ij} -h^{TT}_{2 \, ij} \right) =0 \, .
\label{2t}
\end{eqnarray}
Now that we have at our disposal the full set of equations,
we can study perturbations around  background solutions in the branch one
and two. In the following we will often use the Fourier transform of
perturbations with the respect to $x^i$, the corresponding
3-momentum will be $k^i$ and $k^2 = k^i k_i$. To keep notation as
simple as possible the symbol of the Fourier transform will be understood.

\section{Branch One Perturbations}
\label{br1}

In this case $\xi=\bar \xi$ is a non-vanishing constant such
that $f_2(\bar \xi)=0$, then ${\cal H}_\o={\cal H}$.  From (\ref{2ts}) we can express $\Psi_2$ in
terms of $\Phi_2$, then from (\ref{2tt}) we get that
$\Psi_2=\Phi_2=0$.
Now, using (\ref{2ss}) we have that ${\cal E}={\cal F}_2=0$ and
from the relations in Appendix \ref{rel}, also ${\cal F}_1=0$. At this
point it is straightforward to show that using the equations for the scalar
perturbations of $g$ we get
\begin{equation}
\left[-w \, \Delta  +(3 w+1) \mathcal{H}^2+2
   \mathcal{H}'\right] \Psi _1 +3 (w+1) \mathcal{H} \Psi _1'+\Psi
 _1''=0 \,
\end{equation}
Not surprisingly, this equation describes the very same perturbations
of  GR in the  presence of a fluid with an equation of state $w$.

Also for vectors, being $f_2=0$, again we have the very same equations as in
GR
\begin{eqnarray}
&& \Delta V_{1 \, i} - 16 \pi G \, a^2 \, (\rho + p)  \, \delta v_i  =0 \, ; \\[.2cm]
&&\partial_{(i} V_{1 \, j)}'  + 2 {\cal H}   \partial_{(i} V_{1 \, j)}
=0
\end{eqnarray}
with $V_{2\,i}={\cal V}_{12\,i}=0$. Clearly, as in GR no vector propagates. In the tensor sector four modes propagates.
From the canonical analysis, 8 DOF are expected but only $5=1+4$ are
accounted for. Thus, a scalar plus a vector are not
present and are probably strongly coupled, at least around a FRW
background.  Strong coupling was also found in the Stuckelberg
approach~\cite{Mukopert}. This is not very surprising, condition (\ref{cb1}) in
flat space is equivalent to set to zero the graviton mass and, as
a consequence, both spherically symmetric and FRW branch one solutions
show no gravity modification~\cite{ussphe,uscosm}  and the extra DoF are frozen.
Interestingly enough, in the Stuckelberg approach where  the second
metric is non-dynamical, only the branch one is available and
strong coupling is unavoidable, another manifestation  of the rather
constrained nature of a theory with a priori given metric.

\section{Branch Two: Perturbations in dS Phase }
\label{ds}
Before  analyzing  branch two case  in  full generality, it is instructive to consider a
particular limit of it:  a de Sitter  (dS) background, for which we have
\begin{eqnarray}
&&\rho =\text{const.}\;\;  \Rightarrow \;\; \xi=\text{const.}\;\;
\Rightarrow \;\; c=1 \, ,\;\; f_1=f_2,\;\;\;\; {\cal H}_\o = {\cal
  H}\equiv H\;a \, , \;\;

\\\nonumber
&&{\rm with}\;\;  H=\frac{m}{\sqrt{3\,\kappa}} \sqrt{12\, \xi\,  \left(2\, a_4 \,\xi +a_3\right)+2\,
   a_2+\frac{f_1}{\xi ^2}} \, .
\end{eqnarray}
The dS phase is a fixed point of the FRW geometry of the  branch two solution~\cite{uscosm}.
Introducing
\begin{equation}
\begin{split}
&\Phi_1=\frac{1}{2}(\Phi_+ +\Phi_-), \qquad
\Phi_2=\frac{1}{2\,\kappa\,\xi^2}(\Phi_+ -\Phi_- ) \, , \\
&\Psi_1=\frac{1}{2}(\Psi_+ +\Psi_-),\qquad
\Psi_2=\frac{1}{2\,\kappa\,\xi^2}(\Psi_+ - \Psi_-) \, ;
\end{split}
\end{equation}
after some  tedious computations one can show  that all the equations
in the scalar sector are equivalent to a single second order equation  for $\Phi_-$
\begin{eqnarray}
\Phi _-'' &+&2 \mathcal{H} \, \Phi _-'  \left[\frac{2 k^4}{9 \, a^2 \,
    \mathcal{H}^2 \,
   m_{\Phi }^2+k^4-18 \mathcal{H}^4}-1\right]+\\ [.2cm]\nonumber
&&\frac{1}{3} \, \Phi_- \left[\frac{4 \left(k^6-3 k^4 \,
      \mathcal{H}^2\right)}{9 \,
   a^2 \, \mathcal{H}^2 \, m_{\Phi }^2+k^4-18 \mathcal{H}^4}+3 \, a^2 \,
   m_{\Phi }^2-k^2-6 \mathcal{H}^2\right] =0 \; ;
\label{eqs}
\end{eqnarray}
where
\begin{equation}
m_{\Phi}^2=m^2  \, f_1 \left(\frac{1}{\kappa\,  \xi
  ^2}+1\right)
\end{equation}
is the mass of the scalar field $\Phi_-$. We have also replaced all
space derivatives $\partial_m$ with $i \, k^m$ and $k^2= k^i k^j
\delta_{ij}$.  Defining $\Phi_-= \alpha(t) \, \varphi$, one can choose
$\alpha$ such that the equation for $\varphi$ is canonical
\begin{equation}
\varphi'' + m^2_\varphi \, \varphi = 0 \, ;
\end{equation}
where
\begin{equation}
m_\varphi^2 =\frac{4/3 \,
   k^6+6 k^4 \, \mathcal{H}^2}{9 a^2 \, \mathcal{H}^2 \, m_{\Phi
   }^2+k^4-18 \, \mathcal{H}^4}-\frac{12 k^8 \,
   \mathcal{H}^2}{\left(9 a^2 \, \mathcal{H}^2 \,
   m_{\Phi }^2+k^4-18 \, \mathcal{H}^4\right){}^2}+a^2 \, m_{\Phi
}^2-\frac{k^2}{3}-2 \,
   \mathcal{H}^2 \, .
\end{equation}
In the small $k$ limit we have that $m^2_\varphi>0$ when $m^2_\Phi > 2
H^2$ that is precisely the Higuchi bound~\cite{Higuchi:1986py} in dS
spacetime. In the UV (large $k$), $m^2_\varphi>0$ when  $k^2_{\text{ph}}> 8
H^2$; where $ k_{\text{ph}} = a \, k$. In general, one can check that $m^2_\Phi >
2.3353 \,  H^2$ is sufficient to have $m^2_\varphi>0$  for any $k$.

All remaining fields can be written in terms of $\Phi_-$:
\begin{equation}
\begin{split}
&\Phi_+ = \Psi_+ =0 \, , \qquad \Psi_- =\frac{1}{2\, \mathcal{H}} \left(2
  \Phi _-' -m^2 \,  a^2 \,  f_1 \,  \mathcal{B}_1 \right) \, ;\\[.2cm]
&{\cal B}_1 = \frac{\Phi _- \left(\kappa  \, \xi ^2+1\right) \left(2
\, k^2+3 \, a^2 \,
\, m_\Phi \right)}{3\,  a^2 \, \, \kappa  \, m_\Phi^2 \, \xi ^2 \,
\mathcal{H}}-\frac{2 \, k^2 \, \mathcal{E}}{3 \mathcal{H}}+2 \,
\mathcal{E}' \, ; \\[.2cm]
&{\cal E} = \frac{9 \, \mathcal{H} \left(\kappa  \xi ^2+1\right)
  \left(a^2 m_{\Phi }^2-2 \mathcal{H}^2\right) \, \Phi_- '+
  \left(\kappa  \, \xi ^2+1\right)
  \left[ 3 \left(k^2+3 \mathcal{H}^2\right)
   \left(a^2 m_{\Phi }^2-2 \mathcal{H}^2\right)+2
   k^4\right] \, \Phi_- }{2\,  a^2 \, \kappa \,
   \xi ^2 \, m_{\Phi }^2 \left(9 \, a^2 \, \mathcal{H}^2 \, m_{\Phi
   }^2+k^4-18 \, \mathcal{H}^4\right)} \, .
\end{split}
\end{equation}
As a result, just a single scalar DoF propagates.

For what concerns the vector sector, all  vectors can  be expressed in terms of ${\cal V}_{12 \, i}$
\begin{equation}
V_{2 \, i}=-\frac{m_{\Phi}^2 \,  a^2  \,
   \mathcal{V}_{12 i}'}{ (1+ \xi^2 \,
   \kappa)  ( a^2  \, m^2_\Phi +  k^2)} \, , \qquad  V_{1 \, i} =- \kappa \, \xi^2 V_{2 \, i} \, ,
\end{equation}
with  ${\cal V}_{12 \, i}$ satisfying a second order equation
\begin{equation}
\mathcal{V}_{12 i}'' + \frac{2 \,
   \mathcal{H} \, \mathcal{V}_{12 i}' \left(2  \,
   k^2+a^2 \, m_\Phi^2  \right)}{  \, k^2+ a^2 \, m_\Phi^2}+
\mathcal{V}_{12 i} \left( k^2+ a^2 \, m_\Phi^2 \right)=0 \, .
\end{equation}
In the tensor sector two modes are propagating (4 DoF).
The combination $h_{+\,ij}^{TT} = h_{1 \,ij}^{TT} +\xi^2 \, \kappa  \, h_{2 \, ij}^{TT} $ is massless and satisfies
\begin{equation}
{h_{+ \,ij}^{TT}}''  + 2\,  {\cal H} \, {h_{+ \, ij}^{TT}}' + k^2 \, h_{+ \, ij}^{TT}=0 \, .
\end{equation}
The previous equation is the same for tensor perturbations in GR. While  for the orthogonal combination  $h_{-
  \,ij}^{TT} = h_{1 \,ij}^{TT} - \xi^2 \, \kappa  \, h_{2 \, ij}^{TT}$, we get
\begin{equation}
{h_{- \,ij}^{TT}}'' +2 \, \mathcal{H} \,
   {h_{- \,ij}^{TT}}'+ \left( k^2 + a^2\,  m_{\Phi}^2  \right) \,   h_{- \,ij}^{TT} +
  a^2 \,   m_{\Phi}^2   \frac{\left( \xi^2 \kappa -1\right)}{\left( \xi^2 \kappa +1\right)} h_{+ \,ij}^{TT}=0.
\end{equation}
Summarizing, in the dS phase we have one scalar, one vector and two tensors
that propagate, for  a total of  $1_S+2_V+2_T+ 2_T=7$ DoF,   showing that
all the expected  DoF from the canonical analysis are propagating at
perturbative level. We stress that this is not the case for the branch
one perturbations.
As we will see in the next section, the dynamics of branch two is similar except the
presence of a matter fluid provides an additional scalar DoF.

\section{Branch Two Perturbations}
\label{br2}
The dynamics of branch two perturbations is similar to the dS phase,
only more involved being $\xi$ not constant and $c\neq 1$.
Due to the complexity of the equations it is difficult and physically
not very interesting to study them for generic values of $\xi$.
As shown in~\cite{uscosm} and summarized in section~\ref{frwsec},
from early times to redshift of order one, the massive gravity FRW
background solutions are characterized by  a small  value of $\xi$.
As a result, when $\xi <<1$, the background solutions can be expanded in
series of  the  dimensionless ratio
$\tau/\tau_U \ll1$, where  $\tau_U$  is the  age of the universe in
conformal time. For instance, in the radiation dominated era
\begin{equation}
a = \frac{\tau}{\tau_U} + \epsilon\,\frac{a_0}{10} \,  \left(\frac{\tau}{\tau_U} \right)^5 \, ,
\end{equation}
where $\epsilon=\frac{m^2}{8 \pi  G \rho
  _0}=\frac{1}{3}\,m^2\,\tau_U^2\;$~\footnote{If we believe that our
  theory is
 origin of  Dark Energy we have to take as reference value
$m \sim 10^{-33}\,{\rm eV}\sim H_0$ so that
$\epsilon\sim\frac{\Omega_{\Lambda}}{\Omega_m}$.}.
In Appendix~\ref{corr}, we give the explicit
expressions for the scale factor  $a$ including the leading and   next
to leading terms for both a radiation and matter dominated universe.

An interesting aspect to discuss is the  $m\to 0$ limit.
Naively, taking the formal limit $m \to 0$ in the  equations of motion of
section (\ref{modeq})  we get the perturbed Einstein
equations for two separated GR copies.
Among the perturbations of metric $g$ that is coupled
  with matter, one scalar (induced by the presence matter)  plus two
transverse and traceless  tensors  propagate.
In the sector of the perturbations of $\tilde g$ that have no matter sources, only two tensor modes
propagate. However, when we take into account that,
using the background equations, $\xi$ has
a non trivial dependence on $m$, the very same limit is less
straightforward. Indeed, the branch two background solutions are
characterized by a value of  $\xi$ proportional~\footnote{Recall that
at leading order $\xi=\frac{a_1\,m^2}{8\pi G\,\rho}$.} to $m^2$ and this
completely changes the nature of the  limit $m\to 0$.

In the equations for the $g$  perturbations, see  for instance
(\ref{1tt}-\ref{1ss}),  the coupling with the ones of $\tilde g$ is
through the  effective coupling:
$m^2\,a^2\,f_1$.
In  the small $\xi$ regime, we have
\begin{equation}
 m^2\,a^2\,f_1 \approx
a^2\,a_1\,m^2\,\xi  \approx
 a^2\,\frac{a_1^2\,m^4}{8\,\pi\,G\,\rho_m}\,
 \stackrel{m\to 0}{\to}\,0 \, .
\end{equation}
Thus, in the small $m$ limit,
the perturbations of  the metric $g$   precisely coincide with the
corresponding in GR.
For the equations that govern the perturbation of $\tilde g$, see for
instance (\ref{2tt}-\ref{2ss}),  the effective coupling with $g$ is
$\frac{m^2\,a^2\,f_1}{\kappa\,\xi^2}$.
Then we have that
\begin{equation}
\frac{m^2\,a^2\,f_{1/2}}{\kappa\,\xi^2}
\approx
\, \frac{a^2\,a_1\,m^2}{\,\xi} \,
\approx a^2\,8\,\pi\,G\,\rho_m\,
 \stackrel{m\to 0}{\to}
\,{\rm finite} \, .
\end{equation}
As a result,
$\tilde g$ perturbations are not GR like in the $m \to 0$ limit,
moreover, as we will show they exhibit a non
trivial structure in the momentum $k$ that is  very different from the
linear structure in $k^2$ of GR.
This peculiar behaviour  stems  from the interplay of the branch two background
and the structure of perturbed Einstein equations;
we will return later on this point.

\subsection{Scalar perturbations}
In the scalar sector, all the fields  ${\cal E}, \, {\cal B}_1$
 and $\Psi_{1/2}$ are non dynamical and can   be  expressed in
terms of $\Phi_{1/2}$ that satisfy two second order equations; thus  2 scalar DoF propagate.
Let us consider the case of a radiation  dominated universe. The
equations of motion for the two propagating scalars have the following structure
\begin{eqnarray}
\Phi _a'' &+&\frac{1 }{\tau }\;{\cal D}_{a\,b} \;\;  \Phi _b'+ \frac{1}{\tau^2} \;
{\cal M}_{a\,b}\; \;\Phi _b=0\qquad\qquad  a,\,b=1,2 \, ,
\label{scal}
\end{eqnarray}
where ${\cal D}_{a\,b} $ and ${\cal M}_{a\,b} $ are functions of the
following dimensionless arguments
$\frac{\tau}{\tau_U}$ , $\epsilon$ and $ x = k \, \tau$.
Note that well in the radiation era (and also matter era ), we have
$\frac{\tau}{\tau_U}\ll 1$; thus, we can expand such a complicated expressions obtaining
at leading order
\begin{eqnarray}
\Phi _1'' &+&\frac{4 }{\tau } \;\;  \Phi _1'+ \frac{k^2}{3} \,\; \;\Phi _1+{\cal O}\left(\frac{\tau}{\tau_U} \right)
=0 \, ;\\[0.3cm]\nonumber
\Phi _2'' &+& \frac{10\,x^2+42}{\tau\;(x^2+3)} \;\;  \Phi _2'
+\frac{-5\,x^6-15\,x^4+333\,x^2+999}{3 \, \tau^2\;(x^2+3)^2} \;\;  \Phi _2 -\\&&  \frac{36}{\tau\;(x^2+3)} \;\;  \Phi _1'-
 \frac{3\,(5\,x^2+39) }{\tau^2\;(x^2+3)} \;\;  \Phi _1+{\cal O}\left(\frac{\tau}{\tau_U} \right)
=0 \, .
\end{eqnarray}
The full expressions are lengthy and not particularly illuminating and
are given in  Appendix \ref{ntl} up to the next to the leading order.
We note the various functions ${\cal D}$ and ${\cal M}$ admit a formal expansion in power of $\epsilon$ (i.e $m$)
equivalent on dimensional grounds to an expansion in power of
$\tau/\tau_U$.
Clearly, the equation  for $\Phi_1$ is the same than GR plus small
corrections, while the equation  for $\Phi_2$ has a non trivial
$k\,\tau$ structure whose origin is the  effective coupling with the
metric $g$ proportional to $m^2/\xi$ that does not vanish in the limit $m\to 0$. In order to get some physical insight, let us consider the case $x<<1$
that physically corresponds to modes well outside the horizon. We have
that
\begin{eqnarray}
\Phi_1 &\sim&  const \, ;\\[0.2cm]
\Phi _2'' &+&\frac{ 14}{\,\tau }\, \Phi _2'+
\frac{  37 \,\, \Phi _2-39 \,\,\Phi_1 }{\,\tau^2 }
=0\;\;\Rightarrow \;\;\Phi_2\sim\frac{39}{37}\, \Phi_1=const \, .
\end{eqnarray}
Thus both scalar perturbations are frozen for the modes well outside
the horizon. On the other hand, in the opposite limit, $x>>1$,
e.g. for the modes well inside the
horizon, we have
\begin{eqnarray}
\Phi_1 &\sim& \frac{1}{k^2 \, \tau^{2} }\;\cos k \tau \, ;\\[0.2cm]
\Phi _2'' &+&\frac{ 10  }{\,\tau }\Phi _2'-
\frac{  5\, k^2  }{3 }\Phi _2-
   \frac{36 }{k^2\,\tau^3 } \Phi _1 '  -\frac{  15 }{\tau ^2  }\Phi
   _1=0 \, , \;\Rightarrow
   \;\Phi_2\sim\frac{1}{(k\tau)^{1/2}}e^{+(\frac{5}{3})^{1/2}
     \,k\,\tau}+ {\cal O}(\Phi_1) \, .
\end{eqnarray}
The solution for the homogeneous  part of the $\Phi_2$ equation has
runaway exponentially behavior. Such a tachyonic instability is due
to the sign of the coefficient of $\Phi_2$, positive for super-horizon
perturbations (and then stable) and negative for sub-horizon  perturbation (and then unstable).
For the matter dominate case (see Appendix \ref{matterpert}) the
situation is very similar  and the same kind of instability for the
sub-horizon modes is present. Notice that such an instability is not present in
dS case, see eq. (\ref{eqs}).

The leading contribution in the coefficient of $\Phi_2$ for
sub-horizon  modes ( $x >>1$ ) can be computed for a generic equation
of state   $w$, in the small $\xi$ limit. The result is
\begin{equation}
\left .{\cal M}_{2\,2}\right|_{ x \to \infty}=\left[-  (1+2 \,w)+\frac{2
    \, \left(a_0 \, (w+1) \,\kappa-2 \, a_2\right)}{ \,  a_1}\;\xi
+{\cal O}(\xi^2)\right]\,\, k^2 \, .
\end{equation}
Thus, sub-horizon instabilities are present only when $w>-\frac{1}{2}$
and the $\Phi_2$  perturbation grows exponentially as $e^{(1+2\,w)\,k\,\tau}$.
So, for $w>-\frac{1}{2}$,  the exponential growth of $\Phi_2$ invalidate
perturbation theory at time $\tau \sim 1/k$.  As a consequences,
already in the radiation dominated era sub-horizon perturbations
become  non perturbative, in sharp contrast with GR where matter
perturbations become large only when the universe is non relativistic
due to Jeans instability.
The other scalar fields are given as a function of $\Phi_{1,\,2}$ in Appendix \ref{scalrad}.

\subsection{Vector perturbations}
In the vector sector, using (\ref{vecc}), as in GR, the velocity
perturbation can be easily obtained
\begin{equation}
\delta v_i =\delta v_{0\,i}\;a^{3\,w-1} \, ,
\end{equation}
with  $\delta v_{0\,i}$ an arbitrary  function of $k$.
From (\ref{1vts}-\ref{2vss}) one can show that all vectors can
be expressed in terms of ${\cal V}_{12}$
that satisfies a second order equation given in
Appendix \ref{vect}. Thus, only the  vector  ${\cal V}_{12}$ propagates.
For instance, in the case of a radiation dominated universe we
have at the leading order
\begin{eqnarray}
\delta v&=& \delta v_0(k)=\text{ constant  in time} \, ;\\[0.2cm]
V_1 &=&-\frac{8}{k^2\,\tau^2}\delta v_0 \, ;\\[0.2cm]
V_2&=& \frac{5}{(k^2\,\tau^2+5)}{\cal V}_{12}'-
\frac{40}{k^2\,\tau^2\,(k^2\,\tau^2+5)}\delta v_0 \, ;\\[0.2cm]
{\cal V}_{12}'' &+&\frac{8 \,k^2\,\tau^2+50}{\tau(k^2\,\tau^2+5)}{\cal
  V}_{12}'
+\frac{3}{\tau^2}(k^2\,\tau^2+5)\,{\cal V}_{12}
-\frac{48 \,k^2\,\tau^2+320}{ \,k^2\,\tau^3\,(k^2\,\tau^2+5)}\delta v_0=0
\, .
\end{eqnarray}
Then for super horizon modes with $k\,\tau\ll 1$ we get
\begin{equation}
{\cal V}_{12} = C_1 \,
   \tau^{-\frac{9}{2}-\frac{\sqrt{21}}{2}} + C_2 \, \tau^{\frac{1}{2}
     \left(\sqrt{21}-9\right)}+ \frac{\delta {v_0}}{k^2} \left[\frac{64}{7\,
   \tau} -\frac{16\, \tau \, k^2}{125} \right]  \, ;
\label{solvect}
\end{equation}
where  $C_{1,2}$   are arbitrary functions of $k$.
For any reasonable choice of  $\delta {v_0}$ there is no growing mode.
The structure of the equations is similar in the case of matter
dominated universe.

\subsection{Tensor perturbations}
The  evolution equations for tensor perturbations  in the radiation era
at next to leading order are
\begin{eqnarray}\label{2ten1}
h_1''&+&\frac{2}{\tau}\;h_1'+k^2\;h_1+\epsilon \,\frac{\tau^4}{\tau^4_U}\,\left(\frac{4\,a_0}{5\;\tau}
h_1'\right)=0 \, ; \\[0.2cm]\label{2ten2}
h_2''&+&\frac{10}{\tau}\;h_2'+25\,k^2\;h_2+\frac{15}{\tau^2} \left(h_1-h_2\right)\;+\\
&& \epsilon \,\frac{\tau^4}{\tau^4_U}\,
\left[-\frac{4 \, \left(a_0 \,\kappa-36\,
a_2\right) }{5\, \kappa\, \tau}\,h_2'-\frac{162\, a_2  }{\kappa\, \tau^2}\,h_1+
  \left(\frac{162 \,a_2 }{\kappa\, \tau^2}-\frac{40 \,k^2 \, \left(a_0
   \,\kappa-6\, a_2\right)}{\kappa  }\right)\, h_2\,\right]=0 \, . \nonumber
\end{eqnarray}
Tensor  perturbations $h_1$ of  $g$ behave as in  GR, while  the one
of $\tilde g$, $h_2$, beside a sizable coupling with $h_1$ at early times, show  a larger damping factor
($\frac{2}{\tau}\to\frac{10}{\tau}$) and an  effective  larger mass ($k^2\to 25\,k^2$).
In figure  \ref{f1} we show the numerical solution of (\ref{2ten1}, \ref{2ten2}) .
\begin{figure}
\centering
\includegraphics[height=.4\textwidth]{fig1.pdf}
\caption{Tensor perturbations $h_{1,\,2}$ in a radiation
  dominated universe.
  The initial conditions are set in deep radiation era ($\Omega_m=0.2$, $H=2\,10^{-42}\,GeV$)  at $z=10^{10}$ as $h_1=1$, $h_2=1/4$,
  $h_{1,\, 2}'=0$. }
\label{f1}
\end{figure}
Clearly there are two regimes, depending on the value of
$k\, \tau$. At very early times, when $k\;\tau \ll 1$, the
two fields $h_{1,2} $ are almost  equal and constant
due to the large coupling proportional to $(h_1-h_2)/ \tau^2 $ present
in (\ref{2ten2}).
As soon as $k\;\tau\sim 1$, $h_1$ starts to oscillate and  triggers the oscillations of the $h_2$ sector (and not the opposite!).
Notice that the damping  of $h_2$ is much larger than the one of $h_1$, indeed
\begin{equation}
h_1\sim \frac{1}{\tau}, \quad {\rm while}\quad h_2\sim\frac{1}{\tau^5}
\, .
\end{equation}
During  the matter era, the results are similar.

Summarizing, $h_1$ follows closely GR perturbations; on
superhorizon scales ($k\,\tau\ll1$)  $h_2$ is
proportional to  $h_1$, while  sub-horizon modes are greatly suppressed
($h_2\ll h_1$  when $k\,\tau\gg1$). No instabilities are present.

\section{Conclusions}
\label{con}
In this paper we studied cosmological perturbations around FRW background solutions in
a non-linear ghost free massive gravity   theory.
To construct a massive deformation an auxiliary  metric is mandatory.
In the Stuckelberg approach the extra metric is taken to be a
non-dynamical Minkowski metric. Besides  having an ``absolute''
object that take us back to the time of \ae ther-like theories, such a
theories are rather rigid. For instance, there is no black hole solution
featuring modified Newton potential~\cite{ussphe,DeJac} and  there is no
spatially flat FRW solution~\cite{FRWfroz}-\cite{uscosm}, thus a
spatially negative curvature is required~\cite{uscosm,cur}.
Even if we allow spatial curvature, the resulting solutions feature
an effectively turned off  graviton mass ~\cite{ussphe,uscosm}.
Thus, it is not very surprising that we found the perturbations of
the branch one  are exactly the same as GR.
The extra modes present in the theory  have zero kinetic term and do
not propagate in a FRW background, this is  typical  of strong
coupling and their propagation is expected at  higher order.
Perturbation theory  around branch one solutions cannot be
trusted due to the presence of the strongly coupled
extra modes.
In the Stuckelberg approach branch one solutions are the
only available and nothing more can be said, at least using
perturbation theory.

When the second metric is dynamical, the branch two opens up.
In this case  perturbations  are much richer: all 7+1 expected modes propagate,
and the reliability of perturbation theory results is a non-trivial issue.
In de Sitter all the extra modes propagate and no instability is
present  at all the length scales.
In matter or  radiation dominated period, the background solutions is characterized by a
small $\xi$ value proportional to the graviton mass $m$.
Such a dependence is the origin of deviation from GR in $m\to 0$ limit
with a non trivial $k$ dependence. In particular, the perturbations of the
metric $g$ that couples  with  matter are very similar to the corresponding ones in GR, while $\tilde g$ perturbations
are not GR-like in the $m\to 0$ limit.
Specifically, we found well behaved  perturbations for
all vector and tensor modes, while one scalar mode shows an
exponential  Jeans-like instability  already well in the radiation
epoch, as soon as its wave length enters inside the
horizon. Thus, though $g$ perturbations are well behaved, such a fast
growth drives sub-horizon scalar perturbations into a non
perturbative regime just  after a few Hubble times.

A possible way out might be the introduction of a  mirror (dark) matter
sector minimally coupled to the metric $\tilde g$.
As pointed out in the footnote 3, the small $\xi$ regime is
the source of instabilities and it can be avoided by the presence of
mirror matter reestablishing the normal power counting for
small $m $.
The pressure of mirror fluid can contrast the development of sub-horizon instabilities.
Of course, the analysis of such a bi-metric theory plus  matter and mirror
matter is a totally  different ballpark and it requires a dedicated investigation
that will not be given here, we limit to stress that such an
approach would probably not pass the Occam's razor test.

\bigskip

\noindent {\bf Acknowledgments.}
We thank F. Nesti for many interesting discussions.
\bigskip

\begin{appendix}
\section{Useful Relations}
\label{rel}
One can verify that the following relations among the additional
gauge invariant  scalars hold
\begin{eqnarray}
&&{\cal B}_2= {\cal B}_1 -(1-c^2) {\cal E}'  \, ;\\[.2cm]
&& {\cal H}_\o \, {\cal F}_2 - {\cal H} \, {\cal F}_1 = ( {\cal H} -
{\cal H}_\o ) (\Phi_1 - \Phi_2) \, ; \\[.2cm]
&& c^2( {\cal F}_2+  {\cal F}_1) =( {\cal B}_1 - {\cal E}) ( {\cal H} +{\cal H}_\o)
-2 c^2  (\Phi_1 - \Phi_2)  \, ;\\[.2cm]
&& c^2( {\cal A}_2-  {\cal A}_1) = ({\cal B}_1 - {\cal E}') \left[ c  (
  {\cal H} -{\cal H}_\o ) -c' \right]  \, ;\\[.2cm]
&& c^2( {\cal A}_2+  {\cal A}_1) =2 c^3 \left(\Psi _2-\Psi _1\right)
+\mathcal{B}_1 \left[
   c \left( \mathcal{H}_{\omega }+\mathcal{H}\right) -3 \,  c' \right]+
 3\,  c' \, \mathcal{E}' \\
&&+ c \left[2  \mathcal{B}_1'- 2 \, \mathcal{E}''   -\mathcal{E}'   \left(\mathcal{H}_{\omega
   }+\mathcal{H}\right)\right] \, .
\end{eqnarray}
\section{FRW Background}
\label{corr}

\begin{itemize}
\item During matter era, in the small $\xi $ regime,  we have
$\rho=\rho_0/a^3,\;\;\rho_0\equiv \frac{12}{8 \pi G\,\tau_U^2}$  and for $\tau/\tau_U \ll 1$
\begin{equation}
a= \frac{\tau ^2}{\tau _U^2} + \frac{a_0 \,
   \epsilon }{7 }  \frac{\tau ^8}{\tau _U^8}+ \frac{\tau ^{14} }{ \tau
   _U^{14} } \, \frac{3 \, \epsilon^2 \left(4 \, a_0^2 \, \kappa +49
  \,  a_1^2\right)}{637 \, \kappa } + \cdots \; \, .
\end{equation}
\item During radiation era, in the small $\xi $ regime, we have
$\rho=\frac{\rho_0}{a^4},\;\;\rho_0\equiv\frac{3}{8 \pi G\,\tau_U^2}$ and for $\tau/\tau_U \ll 1$
\begin{equation}
a=\frac{\tau }{\tau _U}+\epsilon\,
\frac{a_0 \, \tau ^5}{10\, \tau_U^5}+
\epsilon ^2\,\frac{ \,
   \left(a_0^2\, \kappa+20\,
   a_1^2\right)}{120 \,\kappa\, }\frac{\tau^9 }{\tau _U^9}+...
\end{equation}
\end{itemize}

\section{Scalar Perturbations in the Radiation Era}
\label{scalrad}

For completeness we give also the leading expressions for the
remaining scalars that can be  expressed in terms of $\Phi_{1/2}$
\begin{eqnarray}
\Psi_1&=&-\Phi _1 \, ,  \qquad\qquad\qquad\qquad
\Psi_2=-\frac{3 \,\mathcal{E}}{5\, \tau ^2}-\Phi _2 \, ;\\[0.2cm]
u_s &=&\frac{1}{2} \tau  \,\left(\tau \, \Phi _1'+\Phi
   _1\right),\qquad
   \frac{\delta \rho}{\rho}=\frac{2}{3} \,\Phi _1 \left(k^2\, \tau ^2+3\right)+2\, \tau \,\Phi
   _1' \, ;\\[0.2cm]
   {\cal B}_2 &=&-60\,\frac{\mathcal{E}}{\tau}-20\,\tau\,\left(\tau \,  \Phi
   _2'+5 \,\Phi _2\right)  \, ;
   \\[0.2cm]
 {\cal E} &=&  -\frac{\tau ^2\, \left(-9\, \Phi _1 \,\left(k^2\, \tau ^2+9\right)+\Phi _2\,
   \left(2\, k^4 \,\tau ^4+15 \,k^2\, \tau ^2+99\right)+9\, \tau  \,\left(\Phi
   _2'-3\, \Phi _1'\right)\right)}{3\, \left(k^2 \,\tau
   ^2+3\right)^2} \, .
\end{eqnarray}

\section{Scalar Perturbations in the Matter Era}
\label{scalmatt}
Leading order of the scalar evolution equations during matter era
\begin{eqnarray}\label{matterpert}
\Phi _1'' &+& \frac{6 }{\tau }\Phi _1
=0 \, ; \\[0.2cm]
\Phi _2'' &+& \frac{4 \left(4 \,x^4+81 \,x^2+720\right)}{\tau\, \left(x
   ^4+18\, x^2+144\right)}\,\Phi _2'+ \frac{-x^6+18\, x ^4+960 \,x^2+11808}{\tau^2 \,\left(x ^4+18 \,x^2+144\right)}\Phi _2-\\ &&
     \frac{6\, \left(x ^4+36\, x ^2+432\right)}{\tau\, \left(x
   ^4+18\, x^2+144\right)}\Phi _1 ' -\frac{x^6+78\, x^4+1728
 \,x^2+14688}{\tau^2 \left(x^4+18\, x ^2+144\right)}  \Phi _1=0 \, .\nonumber
\end{eqnarray}

\section{Next to Leading Corrections for Scalars in  Radiation}
\label{ntl}
For completeness here we give the next to leading correction for the
scalar equations of motion (\ref{scal}).
\begin{eqnarray}
{\cal D}_{1\,1}&=&  4+\epsilon\,\frac{\tau^4}{\tau^4_U}\,\frac{8 a_0    }{45  } +\epsilon^2\,\frac{\tau^8}{\tau^8_U}\,
\frac{4   \,  \left(2\, a_0^2 \,\kappa
   \left(x^2+3\right)^2+25 \,a_1^2 \,\left(4\, x^4+132\,
   x^2+117\right)\right)}{6075 \,\kappa\,
   \left(x^2+3\right)^2} \, ;\\[0.2cm]
{\cal D}_{1\,2}&=&  \epsilon ^2\,\frac{\tau^8}{\tau_U^8}\;\frac{2 \,a_1^2\, \left(5\, x^4+6\, x^2+27\right)
   }{9\,\left(x^2+3\right)^2 \kappa } \, ;\\[0.2cm]
{\cal D}_{2\,1}&=&  \frac{36}{x^2+3}+ \epsilon\,\frac{\tau^4}{\tau^4_U}\frac{4  \, \left(3 \,a_0 \,\kappa  \,\left(x^4+9
   x^2-72\right)+10 \,a_2 \,\left(2 x^6+24 x^4+90
   x^2+81\right)\right)}{15\, \kappa\,    \left(x^2+3\right)^3} \, ;\\[0.2cm]
{\cal D}_{2\,2}&=& \frac{10\, x^2+42}{x^2+3}  \nonumber \\[.2cm]
&-& \epsilon\,\,\frac{\tau^4}{\tau_U^4}\;\frac{4   a_0
    \left(5 x^6+42 x^4+108 x^2+351\right)+40 \,a_2\, \left(4
    x^6+36 x^4+108 x^2+81\right)}{45\, \kappa
  \left(x^2+3\right)^3} \, ;\\[0.2cm]
{\cal M}_{1\,1}&=& \frac{x^2}{3}+  \epsilon\,\,\frac{\tau^4}{\tau_U^4}\;\frac{4 \,a_0}{9\, x^2} +
 \epsilon^2\,\,\frac{\tau^8}{\tau_U^8}\;\frac{  4\, a_0^2\, \kappa\,
   \left(x^2+3\right)^2+45 \,a_1^2 \,\left(3\, x^4+38
\,   x^2+15\right)}{405 \,\kappa\, x^2\,
   \left(x^2+3\right)^2} \, ;\\[0.2cm]
{\cal M}_{1\,2}&=& \epsilon ^2\,\frac{\tau^8}{\tau_U^8}\; \frac{a_1^2 \left(2 x^6+83 x^4+96
   x^2+459\right)}{9\,\left(x^2+3\right)^2
   \kappa} \, ;
    \\[0.2cm]
{\cal M}_{2\,1}&=& 15+ \frac{72}{x^2+3} \\
&-&  \epsilon\,\,\frac{\tau^4}{\tau_U^4}\,\frac{ \, 36\, a_0 \,\kappa\, \left(x^2-27\right)\,
   \left(x^2+9\right) +10 \,  a_2\, \left(8\, x^8+177 \,x^6+1305 \,x^4+3807 \, x^2+3159\right)}{45\, \kappa  \,
   \left(x^2+3\right)^3}\\[0.2cm]
{\cal M}_{2\,2}&=& \frac{333-5 x^4}{3 x^2+9}  +\epsilon\,\,\frac{\tau^4}{\tau_U^4}\,\left(
\frac{4\, a_0 \,  \left(10 x^8+75
   x^6-54 x^4-1323 x^2-8748\right)
   }{405   \, \left(x^2+3\right)^3}
 \right. +\\ && \left.\frac{
 +5\, a_2\, \left(-16 x^8+51
   x^6+1899 x^4+8181 x^2+7533\right)}{405\, \kappa  \,
 \left(x^2+3\right)^3}\right) \, .
\end{eqnarray}

\section{Vector Perturbations}
\label{vect}
Equation of motion of the vector propagating mode
\begin{equation}
\frac{2 \, f_2 \, \kappa  \, k^2 \, \xi ^3 \, \mathcal{H}}{J} \,
\mathcal{V}_{12}'' +\frac{2 \, \kappa
\,    k^2 \, \xi ^2 \, {\cal N}_1 }{J^2} \, \mathcal{V}_{12}'+ f_1 \,
k^2 \, \mathcal{V}_{12} + {\cal N}_0 \, \delta v=0 \, ;
\label{vecteq}
\end{equation}
where
\begin{equation}
\begin{split}
&{\cal N}_1 =2 a^2 f_2 m^2 \left[2 \mathcal{H}^3 \left(\kappa  \xi^4+\xi ^2\right)+4 \xi  \mathcal{H}^2 \xi '+\xi  \xi '
\mathcal{H}'+\mathcal{H} \left(3 \, \xi '^2-\xi \xi
  ''\right)\right] \\
&+\kappa \,  k^2 \, \xi ^2 \, \left[f_2
   \left(4 \xi  \mathcal{H}^2 \xi '+8 \xi ^2
   \mathcal{H}^3+\xi  \xi ' \mathcal{H}'+\mathcal{H}
   \left(\xi '^2-\xi  \xi ''\right)\right)+\xi
   \mathcal{H} f_2' \mathcal{H}_{\xi }\right] \, ,
\end{split}
\end{equation}
and
\begin{equation}
\begin{split}
&J^2 \, {\cal N}_0 = 16 \pi\,  G \,  m^2 \, a^2 \,  \kappa  \, \xi ^2 \,
(w+1) \, \rho _m
\left \{ 2 a^2 f_2^2 m^2 \left[\xi ' \left(\xi  \left(2
   \mathcal{H}^2+\mathcal{H}'\right)+3 \mathcal{H} \, \xi' \right)-\xi \,
\mathcal{H} \, \xi ''\right] \right. \\
&\left. +\kappa  \, f_2 \,
   k^2 \, \xi^2 \left[4 \xi ^2 \mathcal{H}^3+2 \xi
   \mathcal{H}^2 \xi '+\xi  \xi ' \mathcal{H}'+\mathcal{H}
   \left(\xi '^2-\xi  \xi ''\right)\right]+\kappa \,
    k^2 \, \xi ^3 \, \mathcal{H} \, \mathcal{H}_\xi
   f_2'\right \} \, .
\end{split}
\end{equation}
All vectors are expressed in terms of ${\cal V}_{12}$, indeed, omitting the spatial
indices, we get
\begin{equation}
\begin{split}
&\chi = \frac{\kappa\,  k^2\, \xi ^2\, \mathcal{V}_{12}'\,
  \mathcal{H}_{\xi}}{K} -\frac{16 \pi  \,a^2 \,\delta v\, G\, \kappa \, \xi ^2 \,(w+1)
 \,  \mathcal{H}\,\xi  \,\rho }{K} \, , \qquad {\cal H}_\xi = \xi '+2 \,
 \xi \, \mathcal{H} \, ;\\
&K =2 \, m^2 \, a^2 \, f_2 \left[\xi '+\mathcal{H} \left(\kappa \,
    \xi^3+\xi \right)\right]+\kappa  \, k^2 \, \xi^2 \, \mathcal{H}_{\xi } \, ;
\end{split}
\end{equation}
and
\begin{equation}
\begin{split}
&V_1 = -\frac{16 \pi  G \,  a^2 \, (w+1) \, \rho\, \delta v \,\left[2 \, m^2\,
a^2 \, f_2 \left(c\,\xi \, \mathcal{H}\right)+\kappa  \, k^2 \, \xi
^2 \, \mathcal{H}_{\xi}\right]}{K \, k^2}-\frac{2\, \kappa\, m^2 \, a^2 \, f_2  \, \xi ^3 \,
 \mathcal{H} \, \mathcal{V}_{12}'}{K} \, , \\
&V_2 =\frac{2 \,m^2  \, a^2 \, f_2 \left(\xi'+\,\xi
 \, \mathcal{H}\right) \, \mathcal{V}_{12}' }{K}-\frac{32 m^2 \, \pi \, G  \, a^4 \,
   f_2 \,  (w+1) \, \rho \, \left(c\,\xi
   \mathcal{H} \right) \,  \delta v}{K\, k^2} \, .
\end{split}
\end{equation}
\end{appendix}

redpajama_set_name: RedPajamaArXiv


Thank you to Pedal Pushers Farm for your generous discount for the flowers for our flag pole area. We appreciate the help and try to do all of our business locally. The fields are beautiful, thanks to your help!


text:
CARLY RAE JEPSEN ANNOUNCES THE RELEASE OF NEW ALBUM
After the release of her album E•MO•TION in 2015, fans have been waiting for more hits like 'Call Me Maybe' from Carly Rae Jepsen.
Jepsen finally has news! She announced that she'll be releasing her new album titled 'Dedicated' on May 17 via School Boy/Interscope Records.
The full-length album will include her latest releases, 'Now That I Found You' and 'No Drug Like Me'.
Along with the album news, Jepsen also revealed that the Dedicated World Tour is set to kick off on June 27 and finish up on August 10.

redpajama_set_name: RedPajamaCommonCrawl


text:
ACHTUNG BERLIN 2017 Blog: Rakete Perelman
Ahorn | Friday, der 21. April 2017
RAKETE PERELMAN the title of Oliver Aluukas' debut feature film, takes its name from a fictional artist collective out in the countryside of Brandenburg.
We meet them through the character of Jen, a young rebellious woman who, fed up with the bitchy attitude of her job in the fashion industry, sets fire to this year's collection and sets out to escape into the safety of a free spirited artistic community. Or so she thinks.
Arriving in the midst of a crisis, the group is having to come to terms with the fact that living off the grid is not as easy as it sounds. They need to come up with a sizable amount of cash in order to hold on to their living and working space on state owned land. Their one source of income is a contract to perform at an upcoming community fair and feeling themselves under pressure, they decide to scrap their production of "A Midsummer Night's Dream" in favor of something logistically simpler to produce, Ibsen's "Hedda Gabler". Logically, their first choice would have been way more appropriate for an outdoor fête but for the purposes of the movie, Ibsen's collision of doomed relationships provides a more metaphoric vehicle.
We see life in the commune as a series of vignettes of work and play, fun and conflict, as people pair off, listen to music, go swimming, get drunk, take acid, argue over food, get mad at their kids, have lovers quarrels, try (and fail) to have meaningful discussions, and, of course, rehearse the play. Situations and background stories tend to come and go without any real introduction or resolution, and as one might expect, the mounting tensions explode during the performance of the play.
The film means well but didn't really come together for me. It was either too little development to do justice to the characters or too many little plots to function with the slice of life style of the movie. It seemed more like a sort of sketch book of ideas. That being said, I thought Liv Lisa Fries as Jen was a good focal point for the movie and I was surprised how much bigger she appeared on the screen than she seemed when she came up on stage at the end – clearly a strong on-camera presence.
Utopia always looks great but historically never quite works and in that sense the film certainly makes it's point. This group of people who have all come together "to do what they want, the way they want it" finds that they might not be capable of doing either. As Tobias, the director of the play, tells his actors struggling with the conflicting logic of a scene, "We're all afraid. We say one thing but we do something else."
Andrew Horn
Andrew Horn, Berlin-based filmmaker (The Nomi Song, We Are Twisted Fucking Sister!, The Big Blue), producer (East Side Story) and writer, is on the look out for interesting – and not so interesting – movies at this year's edition of Achtung Berlin – new berlin film award.
Films from past editions of the festival can be found in the Achtung Berlin channel on realeyz.de
achtung berlin new berlin film award Berlin brandenburg Ibsen Theater


Over 80 Berklee student clubs enrich the student experience, create a diverse community, encourage involvement, and provide opportunities for students to build valuable skills. Open to all Berklee students, these clubs organize programs, events, and meetings across campus throughout the academic year. Clubs listed here are officially recognized through the Student Activities Center.
Here's a sampling of the clubs created by and available to Berklee students. Student interests are always changing, and so is our list of clubs. To join a club, simply visit its page by clicking on the club's name and send an email to the club email address listed for the club.
Searches club titles and descriptions.
The purpose of the Anime Club at Berklee College of Music is to spread the word about Japanese animated shows and the sub-culture that surrounds it, including the unique type of music. This will allow musicians to explore the type of music that is popular among Japanese teenagers and older fans.
Student Chapter of the Audio Engineering Society, the world's leading organization in Audio Engineering. The Berklee AES Chapter organizes events, workshops, and activities related to the field of audio engineering. We network with other student chapters and participate in the National AES Convention annually.
To perform choral arrangements, both a cappella and with accompaniment, of music from visual media, including film, television, anime, and video game soundtracks.
To promote the appreciation of soundtrack music, which we believe to be a vital part of the Berklee community and the entertainment industry at large.
To celebrate music from visual media by creating new performances, both live and recorded, that will appeal to soundtrack fans around the world.
To provide a venue for our members--who are primarily soundtrack fans--to sing music they love, music they would not have the opportunity to perform in any other setting.
To give our members the opportunity to create original arrangements and hear their arrangements performed by a live choir.
To deepen our own appreciation for soundtrack music and to grow as artists through an intimate acquaintance with music by recognized masters in the field.
Check us out on social media!: Facebook, YouTube, Bandcamp, and Tumblr!
The Berklee A&R Group was founded by MP&E staff member Joe James, a 25-year music industry veteran whose desire is to augment the opportunities within the Berklee community for talented students. On board with Joe are some of Berklee's top students and alumni comprised of business, marketing, and PR specialists, as well as the top producers, engineers, and booking agents.
The team's purpose is to find the very best the Berklee community has to offer and serve as a bridge between Berklee talent and top industry executives. If selected to be represented by the Berklee A&R Group, you will be put with the right team of people to develop your talent and get your music heard by influential people in the music industry.
Berklee Boulders' purpose is to spread the joy of climbing while creating a safe space in which students are able to form new friendships and push themselves both physically and mentally while leading an active, healthy lifestyle. Added to the Berklee community in Spring 2018.
"To have a relationship with God, and relate to others."
The purpose of this club is to create an environment where students can learn about music related gear that is essential in the industry, and allow them to bring in and share gear they are currently using.
Berklee House of Prayer (BHOP) is the official Christian house of prayer at Berklee College of Music, specifically dedicated to uniting Christian students and leaders on campus across all racial, cultural, and denominational lines to pray as one body in unity for each other and the Berklee community.
The Berklee Indonesian Community (BIC) seeks to create more awareness and celebration of the Indonesian culture, amongst students at Berklee, while simultaneously promoting community amongst those from Indonesia.
The goal of this club is to unite the Iranians at Berklee as well as to promote the Iranian culture. The membership will entail meetings that will consist of different cultural aspects of Iran through art, music, film etc. The events of this club will consist of Persian music performances. The events will also include cultural holidays in Iran like Norooz (Persian new year), Yalda (winter solstice celebration), and Mehregan (Persian Festival of Autumn). Added to Berklee in Spring 2018.
Berklee Women in Action aims to create a space and a community where members can bring up topics that affect their everyday lives as young female musicians and women, share resources/books/movies we find inspiring, and explore the ways in which we can bring our art to raise awareness, empower girls and women, and make some changes.
The purpose of Berklee XR is to provide a place for VR, AR and XR enthusiasts to learn, share, collaborate, create projects and talk about the future of these technologies. All related matters to these new technologies are relevant. Formed in Spring 2018.
Our mission is to provide opportunities for the Berklee and Boston Conservatory students with regular recording sessions on campus, throughout the Fall and Spring semesters, with players from both the Berklee and the Boston Conservatory at Berklee. The Orchestra includes a wide variety of majors, including (but not limited to): film scoring, music production and engineering, performance, business, and arts management; members will gain hands-on experience of session clinics and foster collaboration between the two institutions.
The Orchestra will not record or perform any course related materials and all recordings are prioritized to original student work which has not been recorded live before.
The purpose of this club is to help prepare students who have goals of being creators and artists in the popular commercial music industry, by focusing on all aspects of the creation of popular music, including but not limited to arranging, production, songwriting, performance, collaborating and internship opportunities. This shall be achieved through the advisement of club members, faculty and guest speakers.


text:
Por Jogos Pan-Americanos de Winnipeg pode se referir a duas edições diferentes dos Jogos Pan-Americanos realizadas na cidade de Winnipeg, no Canadá:

 Jogos Pan-Americanos de 1967
 Jogos Pan-Americanos de 1999

Desambiguação

redpajama_set_name: RedPajamaWikipedia


text:
Ниже приведён список символов штата Аризона. Большинство символов было выбрано и одобрено в XX веке. Первым из них стал девиз, принятый вскоре после образования территории Аризона в 1864 году. Последним принятым в 2011 году символом стал револьвер Colt Single Action Army. Аризона стала вторым штатом, после Юты с их M1911, имеющим в своих символах огнестрельное оружие. Пятнадцать символов представлены на выставке в музее капитолия Аризоны.

Список символов

Общие

Флора и фауна

Геология

Культура

Примечания
Все официальные символы, кроме минералов, были одобрены и приняты законодательным собранием штата Аризона.
Также к ним относятся Штат ацтеков, Штат-младенец, Штат Валентина, Американская Италия, Штат Песчаных Холмов.
Земноводное было выбрано студентами Аризоны из более 800 вариантов. Среди претендентов колорадская жаба, красно-пятнистая жаба и лопатоноги.
Рассматривались также Ptychocheilus lucius, пустынный карпозубик и Gila elegans.
Другими претендентами были белохвостый олень, пустынный баран и ошейниковый пекари.
Рассматривались также аризонский ядозуб, пустынный западный гофер и жабовидная ящерица.

Источники

Ссылки
Arizona's State Symbols

Аризона
Символы


text:
Уса́дьба Грохо́льских () — комплекс сооружений конца XVIII века, расположенный в ландшафтном парке. Находится в винницком, районе Пятничаны. Построен графом Михаилом Грохольским. Дворец выполнен в стиле раннего классицизма. Рядом находятся два флигеля, павильон и водонапорная башня, стилизованная под средневековую.

История
Усадьба основана в 80-х годах XVIII века польским магнатом графом Михалом Грохольским (1705—1765), сыном брацлавского судьи Францишека Ксаверия Грохольского. Францишек Грохольский приобрёл Пятничаны с приданым жены Анны. Он был крылатым гусаром в войске князя Януша Вишневецкого, где дослужился до поручика. Далее во главе отряда украинской партии боролся с врагами, за что король Август III даровал ему чин ротмистра. Дважды был послом в сейм, среди брацлавской шляхты считался прекрасным знатоком юриспруденции. Собственного особняка не имел, однако женившись на Анне, приданым жены распоряжался разумно, был хорошим хозяином. Его сын, Михал Грохольский, заложил в 1760 году в Виннице костёл и монастырь доминиканцев, а в иезуитском костёле на его средства установили алтарь и амвон. В одном из своих деревень, Терешках, построил часовню.

На строительстве замка работали татарские и турецкие пленные. Планировалось, что усадьба будет представлять собой фортификационное сооружение окруженное прочными каменными стенами с башнями, бойницами и двойными воротами. В результате был возведен одноэтажный квадратный замок, предназначенный для жизни и обороны. В углах поднимались двухъярусные башни. Чуть дальше стояли две квадратные одноярусные башни. От них тянулись валы и рвы, окружавшие крепостной стеной площадь в несколько сотен метров длиной. Еще одна цилиндрическая башня располагалась в месте поворота вала и рва.

После смерти Михала Грохольского в 1765 году после него осталось семеро детей. Имения отца нужно было разделить. Пятничаны, как и Грицевский ключ, дворец в Стрижавке и двор в Виннице, достался старшему сыну Марцину (1727—1807), последнему брацлавскому воеводе. Шляхтич отдавал предпочтение не Пятничанам, а Грицеву. После смерти Мартина его все еще немалые владения снова начали дробиться среди наследников. Пятничаны достались его сыну Михалу (1765—1833). Именно он не только жил в имении на Пятничанах, но и приступил к его реконструкции, так как фортификационные сооружения стали не нужны. Реконструкцией больше занималась его жена Мария, любительница роскоши плохо чувствовала себя в суровых стенах старого замка.

В состав перестроенной усадьбы, размещенной на повышенном плато, с того времени входят дворец, флигель и павильон, расположенные среди старинного ландшафтного парка, частично окруженного старой кирпичной оградой.

В списке землевладельцев Винницкого уезда на 1914 год значатся:
 Грохольский Здислав Станиславович, граф, 4096 десятин, с. Пятничане, Стрижавской волости.
 Грохольский Фаддей Генрихович, 4725 десятин, м. Стрижавка, Стрижавской волости.

Дворец и флигели
Дворец был построен в конце XVIII века. Выстроен в стиле раннего классицизма. Здание дворца кирпичное, прямоугольное, в виде буквы Н, трехэтажное, с боковыми ризалитами на главном и парковом фасадах. Углы здания рустованы. Стены венчает карниз дорического ордера.

Первоначально по обеим сторонам дворца размещались кирпичные квадратные в плане двухэтажные флигели, соединенные с ним одноэтажными полуциркульными галереями с колоннадой (в настоящее время не существуют). Первый этаж главного фасада дворца был акцентирован встроенным между ризалитами шестиколонным портиком с террасой, а окна были оформлены треугольными сандриками. Флигель дворца, конец XVIII века. В конце XIX века к западному, а в середине XX века к северному (заднему) фасадам были пристроены хозяйственные здания.

Сооружение кирпичное, прямоугольное в плане, двухэтажное, с центральным арочным проездом в первом этаже. Главный фасад в традиционной схеме классицизма расчленен спаренными пилястрами тосканского ордера, поднятыми на рустованный цоколь.

Павильон
Павильон (руины), конец XVIII века. Кирпичная, круглая в плане, двухъярусная башня без завершения (не сохранилось), с кладкой под крупный руст. Второй ярус прорезан небольшими оконными проемами с наличниками. В первом ярусе расположено несколько декоративных бойниц.

Памятник составляет комплекс с двухэтажным зданием водокачки конца XIX века, выполненным в романтических формах неоготики из дикого камня (цокольный этаж) и кирпича. Здание в плане — вытянутый прямоугольник с круглой угловой башней, завершенной, как и основной объем, зубцами.

Парк
Парк, занимающий 32 гектара, был создан во второй половине XIX века. Работы по реконструкции парка проводил украинский пейзажист-архитектор Д. Макклер. Характерной чертой его планировки являются многочисленные группы лиственных и хвойных пород. Живописные склоны пруда окружены насаждениями сосны обыкновенной, ели, лиственницы и вековых дубов..

В парке сгруппировано несколько небольших березовых рощ, массивов из белой акации, канадского тополя, ели и других пород. В парке имеются редкие виды деревьев.

Современное состояние

В настоящее время усадьбу занимает эндокринологический диспансер и поликлиника, посещение ограничено. Частично здания отреставрированы.

Адрес
 Украина, Винница, ул. Мичурина, 32.

Примечания

Усадьбы Винницы
Грохольские


Sushi isn't just about cutting the fish and placing it on top of a sushi rice. There is a delicate technique, the right utensils, and knowledge involved in making a god sushi. Let's look at how professionals are making their sushi!
This post mainly talks about how to prepare a fish that has already been cut into a block suited for making sushi or sashimi.
Making a good sushi begins from choosing the right knife.
The knife that is suited for sushi making is about 21 cm long, and should be a 'Japanese Knife'. The kitchen knife that we generally use is called 'ryouba', which means that it is double edged. The traditional Japanese knife, however, is single-edged, and it is suited for slicing rather than cutting. This structure allows the user to slice off pieces without pressuring the ingredients, keeping the particles from breaking and umami from escaping. Because of its sharpness, it can also leave a certain gloss on the cross section of the fish that helps sushi look more appetizing.
You can also use your kitchen knife if it's sharp enough, but since normal kitchen knife tends to take away the gloss and sometime even cause a rough or uneven surfaces, so knives such as 'gyuto' and 'yanagiba' are recommended.
Toppings on sushi is called 'neta'. When you cut these neta from a fish block called 'saku', the first thing you have to be careful about is the direction of the tendons. In general, if you're cutting from a large fish like tuna or swordfish, your knife should be intersecting the tendons in order to lessen the toughness and rough textures.
When you're dealing with a smaller fish or fish with tendons that are already starting to fall apart, however, it is better to place your knife parallel to the tendons to get a clean peace. In this case, you don't need to worry about the toughness of the tendons because they're not as thick as those from the bigger fish.
Now to the actual cutting!
When you hold the knife, rest your index finger on the back of the knife (pretend that the tip of your knife is your finger!).
Place the heel of the blade so that the thickness would be around 0.5mm for soft fish such as tuna, 0.2mm for tougher fish like sea bream, and pull the full length towards you. The knife should be slightly diagonal as shown in the picture.
At this point, please do not completely slice the piece off yet. Without pulling the knife back out, put it back into a vertical position, and cut off the piece. This is called 'koba-gaeshi'. It's not a must, but it's a nice touch to make sushi look more appetizing.
Although the steps in making a sushi is similar between a lot of the toppings, how the chefs choose and prepare the fish can be slightly different depending on the sort of sushi they are making. Again, this isn't a must, but it sure does add to the taste of your sushi.
Sometimes it's hard to cut salmon if it's rich in fat. In that case, sprinkle some salt on the surfaces of the salmon. Wait for 10 minutes, wash the salt off with water, and wipe the water off. That should prevent the salmon from slipping on the cutting board (some chefs say that this process makes the salmon taste better too).
For salmon, cut the meat so that the knife is parallel to the tendons.
Be careful with any thick tendons, because the piece can create a crack if the knife gets stuck in between the cutting. If the tendons are starting to fall apart, put the knife in parallel to the tendons, but otherwise cut it so that the knife intersects the tendons.
There's so much more to making a perfect sushi, so if you're interested, please check out other pages on this blog!


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(1443) Ruppina ist ein Asteroid des Hauptgürtels, der am 29. Dezember 1937 vom deutschen Astronomen Karl Wilhelm Reinmuth entdeckt wurde, der am Observatorium auf dem Königstuhl bei Heidelberg tätig war.

Benannt ist der Asteroid nach der Stadt Neuruppin in Deutschland, dem Geburtsort des Astronomen Martin Ebell.

Siehe auch
 Liste der Asteroiden

Einzelnachweise

Hauptgürtelasteroid unter 50 km Durchmesser


In a recent article about how to write a SELinux Compliance Policy you learned how to use CloudForms' and ManageIQ's capability to perform compliance checks. This article goes one step further: Instead of just reporting compliance or non-compliance of a given virtual machine, we use the power of Ansible to enforce compliance.
This example builds on the Compliance and Control policy described in the mentioned article and it is recommended to read it first.
Enterprises often have rules and regulations about system compliance. This could include a specific baseline configuration, for example hardening rules. It could also include other requirements, like backup and monitoring has to be configured, a proper license has to be available (particularly with proprietary software) and more. Compliance checks in CloudForms and ManageIQ can bundle these requirements into policy profiles.
If one or more of the requirements is not met, actions can be triggered. The most obvious and most simple to implement is to mark the system as being "non compliant".
Compliance policies can also trigger other actions, including running an Ansible Playbook or perform a custom method, which allows us to run our own (Ruby) Method as an action.
A GitLab repository with CloudForms Ansible Playbooks optimized for the usage with CloudForms and ManageIQ has to be added to Tower first. This repository contains a Playbooks called "selinux-enforcing" which makes sure the SELinux modus is set to "Enforcing".
Next we force an update of the Ansible Tower inventory. Navigate to Automation, Ansible Tower and Explorer. Select your Tower Provider and click on Configuration, Refresh Relationships and Power State. Such a refresh is executed in the background and can take a minute or two. Eventually the new Job Template should show up in the accordion on the left.
To trigger an execution of an Ansible Playbook from a Control or Compliance Policy, we first have to create a new Action. Navigate to Control, Explorer. In the accordion on the left, click on Actions and from there Configuration, Add a new Action.
Note: The Name "Fix SELinux" has to match the name of the Job Template definition in Ansible Tower, or the Action will fail.
If you want to use the native support to run Ansible Playbooks, it's important to make sure the Embedded Ansible Role is enabled. Without this Role properly running, Ansible Playbooks can not be executed and it is not even possible to add an Ansible Playbook Repository. A good article summarizing the how to Debug Ansible Automation inside Red Hat CloudForms has just been published by my buddy Victor.
After ensuring the Role is properly configured, add the CloudForms Ansible Playbooks repository found on GitLab.
This blog post is not going into details on how to do this. I already created a lab called Getting well with CloudForms which covers the embedded Ansible capabilities.
To use the previously created Action in the Compliance Policy, navigate to Control, Explorer first. Then navigate to the Compliance Policy and the respective event. Add the Action you created in the previous step to the "Order of Actions if ANY Conditions are False" list.
I uploaded an example VM-Security-Profile-with-Ansible-Action on Github.
To do a test run, you can either power on a VM, or "Perform Smart State Analysis" from the VM Configuration menu.


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O'Dea Cross Country
The O'Dea High School Cross Country Team is a non-cut Fall sport that welcomes runners of all abilities. The XC squad features a unique community with all grade levels, Freshman through Senior, competing and training together. With a focus on hard work and personal accountability, our athletes set out to achieve both individual and team goals in the spirit of a proud tradition of accomplished O'Dea distance runners.
In 2014 Andy Slatt, former O'Dea cross country coach, was inducted into the Washington State Cross Country Hall of Fame having already been inducted into the O'Dea Athletic Wall of Honor in 2010. Slatt's former runner, David Bazzi (class of '96) now coaches the team and looks to continue Coach Slatt's focus on competition and teamwork.
Racing from 2 miles to 5km in the highly competitive Metro League, the Fighting Irish look forward to new challenges and successes in the year to come.
There are no announcements at this time. GO IRISH!
A 1996 O'Dea graduate, Coach David Bazzi returned to O'Dea in 2010 to take over the program from retiring O'Dea and Washington State Hall of Fame Coach, Andy Slatt. In his six years, Coach Bazzi has coached numerous state qualifiers while continuing Coach Slatt's legacy of guiding his athletes into the collegiate ranks with athletes competing at West Point, University of Portland, University of Chicago, PLU and Xavier.
While at O'Dea as an athlete, Bazzi competed at the state meet six times in cross country and track & field, was a member of the 1995 State champion track team and was runner-up in the 1996 state 3200m race prior to earning All-American honors in the 2 mile race later that season. Bazzi went on to compete at the University of Washington, earning 2 collegiate All-American honors, breaking 3 UW School records (Outdoor: 10k,5k. Indoor: 5k), and winning a Pac-10 Championship in the 2001 10,000m race. He was also selected as a member of US National Team for the 2001 World University games in Beijing, China where he competed in the half-marathon event. In 2016 Bazzi was inducted into O'Dea's esteemed Wall of Honor.
David and his wife Kara live in North Seattle with their two daughters, Sophia and Hannah.
For more information about Irish Cross Country please contact O'Dea Athletic Director, Monte Kohler, at (206) 624-2068 or odad@odea.org.
Metro League Champions
Academic State Champions