text:
\section{Introduction}

	For the past decades, inflation has become the most popular scenario to describe the very early universe. It can solve the horizon problem and flatness puzzles in the hot big bang~\cite{ Guth:1980zm,Linde:1981mu,Albrecht:1982wi,Starobinsky:1980te}. Inflation predicts the primordial density fluctuations, which shows excellent agreement with experimental data from Large Scale Structure (LSS) and Cosmic Microwave Background (CMB).\\

	However, many alternative to inflation scenarios were also proposed in the literature. For example, slow contraction scenarios such as the Ekpyrosis~\cite{Khoury:2001wf}, fast contraction scenarios such as matter bounce~\cite{Wands:1998yp,Finelli:2001sr}, and slow expansion scenarios such as~\cite{Piao:2003ty}, string gas cosmology~\cite{Brandenberger:1988aj,Nayeri:2005ck}, or Galilean genesis~\cite{Creminelli:2010ba,Wang:2012bq}. \\

	For both inflation and alternative to inflation scenarios, a large number of models can be built, with a wide spectrum of predictions. To figure out the expansion (or contraction) history of the universe, and distinguish inflation from alternatives, it may be more efficient to start not from the model details, but rather model-independent features purely from the time-dependence of the scale factor, which is the defining features of inflation or an alternative scenario. One example is the primordial gravitational waves \cite{Starobinsky:1979ty} which are the tensor part of the primordial fluctuation, and it may be observed in the CMB experiment from B-mode polarization. Another possible way is to use massive fields that existed in the primordial universe~\cite{Chen:2009we,Chen:2009zp,Baumann:2011nk,Arkani-Hamed:2015bza}. The classical \cite{Chen:2011zf, Chen:2011tu} or quantum \cite{Chen:2015lza, Chen:2016cbe, Chen:2016qce} oscillations of massive fields work as primordial standard clocks which can directly record the time evolution of the scale factor $a(t)$.

	In primordial standard clocks, the mass parameter is regarded as time-independent. However, non-standard clocks with time dependent mass are also discussed \cite{Chen:2011zf, Huang:2016quc, Domenech:2018bnf}. For the case of inflation, though it is natural to consider time-independent mass due to the approximate scale invariance of inflation, exceptions arise from mass terms arising from interactions~\cite{Domenech:2018bnf}, or interactions without a mass term~\cite{Huang:2016quc}. For alternative scenarios, in addition to a fixed mass parameter, a mass of order Hubble parameter may be more naturally generated in a dynamical way. The Hubble parameter is strongly time-dependent in alternative to inflation, and thus provides significant time dependence to the mass of the field.\\

	In this work, we study those non-standard clocks with time-dependent mass in alternative scenarios. Generally, the time-dependent mass can be generated from two different mechanisms. Firstly, the massive fields have the non-minimal coupling with Ricci curvature $R$ such as $\xi R\sigma^2$. In the inflation case, the background is approximately de-sitter geometry and thus Ricci scalar contributes to the effective mass time-independently (proportional to $\xi H ^2$). However, in alternative to inflation scenarios, this term can generate a time-dependent mass. Another mechanism is from quantum loop correction. As we know in de-sitter case, with a self-interaction $\lambda \sigma^4$, due to the strange IR behaviors it can generate an effective mass $m_{\mathrm{eff}}^2\propto  H^2$ for scalar fields~\cite{Starobinsky:1994bd,Finelli:2008zg,Burgess:2009bs,Burgess:2010dd,Rajaraman:2010xd,Beneke:2012kn,Marolf:2010zp,Chen:2016nrs,Chen:2016uwp,Chen:2016hrz}. By introducing this simple self-interaction $\lambda \sigma^4$ into alternation to inflation scenarios, it may also generate a time-dependent effective mass. Following the standard procedure to calculate correlation functions, we show that with a time-dependent mass, the clock signal is different from previous works.
	\\

	The paper is organized as follows: We briefly review the concept of quantum standard clocks in section~\ref{sec2}. Then in section~\ref{sec3} and~\ref{sec4} we discuss the quantum non-standard clock signal with time-dependent mass generated from Ricci scalar and self-interaction term respectively. We summarize in section~\ref{con}.

	\section{Quantum standard clocks}\label{sec2}
	\subsection{Quantum fluctuations of massive fields}
	Cosmological scale factors are expressed as power law functions with different index $p$ to describe possible conditions,
	\begin{align}
	a(t) = a_0     \left(\frac{t}{t_0}\right)^p~,
	\end{align}
	where $a_0$ and $t_0$ are constants. The Hubble parameter is thus $H = \frac{\dot{a}}{a} = \frac{p}{t}$.
	In arbitrary FRW time-dependent background, the equation of motion of massive scalar field is
	\begin{align}
	\delta \ddot \sigma + 3H \delta \dot \sigma - \frac{1}{a^2} \partial_i^2 \delta\sigma + m^2 \delta\sigma = 0~,
	\end{align}
	or expressed by the conformal time $\tau$, which is related to t by $a \tau = \frac{t}{(1-p)}$,
	\begin{align}\label{masseom}
	\delta\sigma'' + 2Ha \delta\sigma' - \partial_i^2 \delta\sigma + m^2 a^2 \delta\sigma = 0~.
	\end{align}
	We are interested in the massive fields in the classical regime where the long wavelength mode satisfies $\frac{k}{a} \ll m$. And the equation of motion can be approximated as
	\begin{align}
	\ddot v_k + 3H \dot v_k + m^2 v_k = 0~.
	\end{align}
	This classical-like behavior is necessary for the quantum standard clock for contraction scenarios.
	\subsection{Quantum standard clocks}
	As the standard clock, the massive field oscillates to record the evolution of scenarios. The curvature mode resonates with the massive clock field when their wavenumbers match with each other. In an arbitrary time-dependent background, the mass of the massive scalar field is larger than scale of horizon, which causes  oscillation as $ \propto e^{\pm i m t}$ with approximated constant frequency.\\

	The quantum fluctuation of the massive field occurs as the standard clock in the time-dependent background. It can generate the clock signal with curvature modes $u_k$ with the oscillation $e^{ -iK\tau}$. In order to clarify the properties of it, we consider the two coupling terms between the perturbation of curvature field $\zeta$ and clock field $\delta \sigma$. The bilinear coupling is used as $L_2 \propto c'_2 a^3 \delta\sigma \dot{\zeta} $ and the cubic coupling is $L_3 \propto c'_3 a^3 \delta\sigma \dot{\zeta}^2 $, where $c_2'$ and $c_3'$ represent coupling constants.\\

	By using the in-in formalism \cite{Weinberg:2005vy, Chen:2010xka, Wang:2013zva}, the three-point function of the curvature perturbation can be written as \cite{Chen:2015lza}
	$$ \langle \zeta^3 \rangle ' \ \supset \  \int_{t_0}^{t} d \tilde{t_1} \int_{t_0}^{t} dt_1\langle0|H_I(t_1)\zeta_I^3 H_I(\tilde{t_1})|0\rangle'  $$
	$$- 2\mathrm{Re}\left(\int_{t_0}^{t} dt_1 \int_{t_0}^{t_1} dt_2 \langle 0|\zeta_I^3 H_I(t_1) H_I(t_2)|0 \rangle'\right)$$
	\begin{align}
	= 2 u_{k_3}^{*} u_{k_1} u_{k_2} |_{\tau = 0} \left(\int_{-\infty}^{0} d\tau c_2' a^3 v_{k_3}
	u_{k_3}'\right)\left(\int_{-\infty}^{0} d\tau c_3' a^2 v_{k_3}^{*} u_{k_1}^{'*} u_{k_2}^{'*}\right)
	\end{align}
	$$ -2 u_{k_3} u_{k_1} u_{k_2}|_{\tau = 0}$$
	\begin{align}
	\times\left(\int_{-\infty}^{0} d\tau_1 c_2' a^3 v_{k_3} u_{k_3}^{'*} \int_{-\infty}^{\tau_1} d\tau_2 c_3' a^2 v_{k_3}^{*} u_{k_1}^{'*} u_{k_2}^{'*}\right.
	\end{align}
	\begin{align} \left. +\int_{-\infty}^{0} d\tau_1 c_3' a^2 v_{k_3} u_{k_1}^{'*} u_{k_2}^{'*} \int_{-\infty}^{\tau_1} d\tau_2 c_2' a^3 v_{k_3}^{*} u_{k_3}^{'*}\right)
	\end{align}
	$$+ \mathrm{c.c.} + 2 \ \mathrm{perms}~.$$
	Here, $u_k$ and $v_k$ denote the mode functions of $\zeta$ and $\delta\sigma$. The prime refers to the expression without the common factor $(2\pi)^3 \delta{(\Sigma_i \mathbf{p_i})}$. The term ``$2 \ \mathrm{perms}$'' represents the permutation $k_1 \leftrightarrow k_3$ and $k_2 \leftrightarrow k_3$.

	\subsection{The alternative scenarios $(0 < p < 1)$}
	The relations of scale factor can be deduced from (2.1)
	\begin{align}
	a = a_0 \left(\frac{\tau}{\tau_0}\right)^{\frac{p}{1-p}}, \ \ \tau= \frac{1}{1-p}\frac{t_0^p}{a_0} t^{1-p}~.
	\end{align}
	When two modes resonant, massive fields satisfy the classical regime conditions and the curvature mode is still sub-horizon. For the generation of the clock signal, we need two short curvature modes at the sub-horizon region. We choose $\tau_0 = -1$ for simplified calculation. By choosing Bunch-Davies (BD) vacuum under the squeezed limit $k_3/k_{1,2} \rightarrow 0$, the mode function of curvature mode can be approximately as
	\begin{align}
	u_k  \propto \frac{1}{(-\tau)^{\frac{p}{1-p}}} e^{-i k \tau}.
	\end{align}

	For the case of constant mass parameter $m$, the mode function can be represent as
	\begin{align}
	v_k \propto \frac{1}{(-\tau)^{\frac{3p}{2(1-p)}}}\left[c_{+}e^{i (1-p)a_0 m (-\tau)^{\frac{1}{1-p}}} + c_{-}e^{-i (1-p)a_0 m (-\tau)^{\frac{1}{1-p}}}\right]~.
	\end{align}
	In this equation, the mass of the field is assumed time-independent. However, when the background has no scale invariance, the mass of the field could naturally be time-dependent. The generalization $m=m(t)$ can change the predictions of the quantum clocks into non-standard ones.

	\section{Time-dependent effective mass from coupling to Ricci curvature} \label{sec3}

	\subsection{The effective mass}
	The non-minimal coupling between the Ricci curvature $R$ and the scalar field $\sigma$ can be considered as a time-dependent contribution to the effective mass. The total effective mass $\mu$ is
	\begin{align}
	\mu^2 = m^2 + \xi R~,
	\end{align}
	where $\xi$ is the coupling constant of the non-minimal coupling, and the original mass $m$ is a constant. The total effective mass should be a combination of these two contributions.

	The Ricci scalar of the FRW metric is
	\begin{align}
	R

	=  6 \left[\frac{\ddot{a}}{a} + (\frac{\dot{a}}{a})^2\right]~.
	\end{align}
	We consider the scale factor $a$ as a time-dependent monomial function $a(t) = a_0 (\frac{t}{t_0})^p$ so
	\begin{align}
	R = 6 \frac{p (2p-1)}{t^2}~,
	\end{align}
	\begin{align}
	\mu^2 = m^2 + 6\xi \frac{p(2p-1)}{t^2}~.
	\end{align}
	For alternatives scenarios with time-dependent mass, we consider the differential equation of scalar perturbation for the classical regime. We will discuss the general form in \ref{eom}. For simplification, we here focus on the parameters such that the bare mass $m$ is small, though the transition between a constant mass and a dynamical mass may be interesting, similar to the discussions in \cite{Chen:2018cgg}. Neglecting $m$, and using the relation $\tau= \frac{1}{1-p}\frac{t_0^p}{a_0} t^{1-p}$, we rewrite the time variable of the differential equation into conformal time,
	\begin{align}
	\frac{d^2 v_k}{d\tau^2}+\frac{2p}{\left(1-p\right)\tau}\frac{dv_k}{d\tau}+\left[6\xi\frac{p\left(2p-1\right)}{\left(1-p\right)^2\tau^2}\right]v_k= 0~.
	\end{align}
	The general solution is
	\begin{align}
	v_k(\tau) \rightarrow C_1\left(\frac{\tau}{\tau_{k}}\right)^{\frac{\sqrt{\frac{3}{2}}\sqrt{p\left(2p-1\right)}\sqrt \xi\left(-A+B\right)}{-1+p}} + C_2 \left(\frac{\tau}{\tau_{k}}\right)^{\frac{\sqrt{\frac{3}{2}}\sqrt{p\left(2p-1\right)}\sqrt \xi\left(A+B\right)}{-1+p}}~,
	\end{align}
	where $A$ and $B$ are
	\begin{align}
	A=\frac{1}{6}\sqrt{-144-\frac{36}{\left(2p-1\right)\xi}+\frac{6}{p\left(2p-1\right)\xi}+\frac{54p}{\xi\left(2p-1\right)}}~,
	\end{align}
	\begin{align}
	B = \frac{-\sqrt6\sqrt{\left(2p-1\right)p}+3\sqrt6p\sqrt{\left(2p-1\right)p}}{6p\left(2p-1\right)\sqrt \xi}~.
	\end{align}
	Here, $t_k$ refers to the time at $a(t_k) = k/m$ for one boundary of the resonance.
	\subsection{Appropriate range of p}
	An oscillating massive field is required for generating the clock signal, which restricts the range of $p$ in (3.7). In this case, not all alternative scenarios could generate the clock signal. With $\xi > 0$, the power index
	\begin{align}
	\frac{ \sqrt{\frac{3}{2}}\sqrt{p\left(2p-1\right)}\sqrt{\xi}\left(\pm A+B\right)}{p-1}
	\end{align}
	must contain an imaginary part to make sure the oscillation. \\
	From (3.9), the index $B(p)$ cannot make any contributions to the imaginary part in any scenarios since
	\begin{align}
	\mathrm{Im}\left[\sqrt{p(2p-1)} B \right]=\mathrm{Im}\left[\frac{\sqrt6\left(2p-1\right)p+3\sqrt6p\left(2p-1\right)p}{6p\left(2p-1\right)\sqrt \xi}\right] = 0~.
	\end{align}
	The index $A$ will only remain the imaginary part when it satisfies
	\begin{align}
	-144-\frac{36}{\left(2p-1\right)\xi}+\frac{6}{p\left(2p-1\right)\xi}+\frac{54p}{\xi\left(2p-1\right)} < 0~.
	\end{align}
	We should make sure the existence of an imaginary part in $\sqrt{p(2p-1)A}$ to generate the oscillatory field. The allowed interval of $p$ depends on the value of coupling coefficient $\xi$. For $\frac{1}{6} < \xi < \frac{3}{16}$, $p$ satisfies
	\begin{align}
	\frac{4 \xi -1}{16 \xi -3}-2 \sqrt{\frac{2}{3}} \sqrt{\frac{6 \xi ^2-\xi }{(16 \xi -3)^2}}< p<2 \sqrt{\frac{2}{3}} \sqrt{\frac{6 \xi ^2-\xi }{(16 \xi -3)^2}}+\frac{4 \xi -1}{16 \xi -3}~.
	\end{align}
    For the case $\xi = \frac{3}{16}$, $p$ should be larger than 2/3. And for the cases $\xi > \frac{3}{16}$,
    \begin{align}
    p < \frac{4 \xi -1}{16 \xi -3}-2 \sqrt{\frac{2}{3}} \sqrt{\frac{6 \xi ^2-\xi }{(16 \xi -3)^2}} \ \ \  \mathrm{or}\ \ \ p>2 \sqrt{\frac{2}{3}} \sqrt{\frac{6 \xi ^2-\xi }{(16 \xi -3)^2}}+\frac{4 \xi -1}{16 \xi -3}~.
    \end{align}
	Notice that the cases for $\xi \leq \frac{1}{6}$ is not allowed. When $\xi = \frac{1}{6}$, it leads to the conformally invariance of the Klein-Gordon equation containing the effective mass with $m = 0 $, which has no oscillatory clock signals. This is expected since a conformally coupled field does not ``know'' the FRW expansion of the universe (which is conformally Minkowski).\\

	We show the allowed ranges of $p$ related to different choices of $\xi$ in Figure~\ref{fig1}. Here we only consider the scenarios with $-1<p<1$. In this figure, we redefine the R.H.S. of (3.12) as the function $F(\xi)$ and the L.H.S as $G(\xi)$, which is related to the dark yellow and blue lines in the Figure~\ref{fig1}. For $p>0$, We can figure out that the allowed $p$ should be always larger than 1/2, which is the limit for the $\xi \rightarrow \infty$ case. Thus, slow contraction scenarios will not generate such non-standard clock signals from non-minimal couplings. But the slow-expansion scenarios are allowed for some ranges of $\xi$.

		\begin{figure}[hptb]
			\centering
		\includegraphics[width=0.8\textwidth]{figurepxi.pdf}
		\caption{Choices of $p$ and $\xi$. In this figure, the gray shadow parts corresponds to the choices of $p$ and $\xi$ where there is oscillatory clock signal. The dark green line represents for the discussion boundary  $\xi = 3/16$. \label{fig1} }
	\end{figure}

	\subsection{The non-time-ordered integral}
	According to Eq.(2.9) and (3.6), the mode functions are
	\begin{align}
	v_k(\tau) \rightarrow \left( \frac{\tau}{\tau_{k}} \right)^{\frac{1-3p}{2-2p}}\left[e^{i S \mathrm{log}(-\tau)} C_1 + e^{-i S \mathrm{log} (-\tau)} C_2\right]~,
	\end{align}
	\begin{align}
	u_k(\tau) \rightarrow \frac{1}{\sqrt{k} (-\tau)^{\frac{p}{p-1}}} e^{-i k \tau}~,
	\end{align}
	where
	\begin{align}
	S = \frac{\sqrt{(48\xi - 9) p^2 + 6(1-4 \xi)p -1}}{2(p-1)}~.
	\end{align}
	For non-time-ordered integral Eq.(2.5),  the resonance among these fields can only occur in the second term inside the second parenthesis. To describe the property of this term qualitatively, we use the method of saddle point approximation which we left more details in Appendix B. For the curvature field mode $u_k$,
	\begin{align}
	u_k \propto \frac{1}{\sqrt{k} (-\tau)^{\frac{p}{1-p}}} e^{- i k \tau} \ \ \Rightarrow \ \ u_k' \propto \frac{1}{\sqrt{k}}(-\tau)^{-\frac{p}{1-p}} [-\frac{p}{(1-p)\tau} - ik] e^{- i k \tau}~.
	\end{align}
    The most important resonance term is
	\begin{align}
	\int_{-\infty}^0 d\tau c_3' a^2 v_{k_3}^{*} u_{k_1}^{'*} u_{k_2}^{'*}~.
	\end{align}
	We notice that only the second term of Eq.(3.15) with coefficient $C_2$ can form the resonance. So the above integral should be proportional to
	\begin{align}
	\sim C_2\int_{-\infty}^0 d\tau \left(\frac{\tau}{\tau_{k_3}}\right)^{\frac{1-3p}{2-2p}}\frac{\left[-\frac{p}{(1-p)\tau}+i k_1\right]^2}{k_1} e^{i[S \mathrm{log}(-\tau)+ 2 k_1 \tau]} ~,
	\end{align}
	where the parameter $\tau_{k_3}$ is assumed to satisfy
	\begin{align}
	a(\tau_{k_3}) = \frac{k}{\mu_{\mathrm{eff}}} \ \ \Rightarrow \ \ \tau_{k_3}  = -\frac{\sqrt{6 \xi p (2p-1)}}{1-p}  \frac{1}{k_3}~.
	\end{align}
	Under the squeezed limit $k_3/k_{1,2} \rightarrow 0$, resonance happens when the conformal time $\tau_{*}$ satisfies
	\begin{align}
	\frac{d}{d \tau} (S\  \mathrm{log}(-\tau) + 2k_1 \tau) = 0~\bigg|_{\tau=\tau_{*}} \ \ \Rightarrow \ \ \tau_{*} = - \frac{S}{2} \frac{1}{k_1}~.
	\end{align}
	According to the method of saddle point approximation, the integral describing the resonance should be proportional to
	\begin{align}
	\sim C_2 \Omega\
	\mathrm{exp}\left\{ i S \  \mathrm{log}\left[\omega\left(\frac{2k_1}{k_3}\right)^{-1}  \right] - i S \pm  i \frac{\pi}{4}\right\}  \left(\frac{2k_1}{k_3}\right)^{\frac{3p-1}{2-2p}}~.
	\end{align}
	The parameters $\Omega$ and $\omega$ denotes
	\begin{align}
	\Omega(p, \xi) = \omega^{\frac{3p-1}{2-2p}}\sqrt{\frac{\pm \pi S}{2}}\left[i + \frac{2 p }{(1-p)S}\right]^2~,
	\end{align}
	\begin{align}
	\omega(p , \xi) = \frac{\sqrt{6 \xi p (2p-1)}}{(1-p)S}~.
	\end{align}
	We collect the $k_1$-independent parameters into $f(p, \xi,k_3)$ and $\phi(p, \xi, k_3)$, which depends on the details of alternative to inflation models. In general, the coefficient $C_1$ and $C_2$ may depend on $k_3$. This introduces parts of $k_3$ dependence in the prefactor $f(k_3)$ and the phase $\phi(k_3)$. We also assume $u_{k_i}\big|_{\tau=0}$ to be proportional to $1/\sqrt{k^3_i}$ .  So the non-time-ordered integral is
	\begin{align}
	\propto f(p, \xi,k_3 )\left( \frac{2k_1}{k_3}\right)^{\frac{3p-1}{2-2p}} \mathrm{exp} \left\{ i S \ \mathrm{log}\left[ \left(\frac{2k_1}{k_3}\right)^{-1}\right] + i \phi(p , \xi, k_3) \right\}~.
	\end{align}
	Under the squeezed limit $k_3/k_{1,2}\rightarrow 0$, the clock signal is considered as the oscillatory shape function in the three function in the previous work. It is defined as
	\begin{align}
	\langle \zeta^3 \rangle \equiv S(k_1, k_2, k_3) \frac{1}{(k_1 k_2 k_3)^2} (2\pi)^7 \tilde{P}_{\zeta}^2 \  \delta^3(\sum_{i=1}^3 \textbf{k}_k)~,
	\end{align}
	where the fiducial power spectrum is $\tilde{P}_{\zeta} \equiv 2.1 \times 10^{-9}$. So the clock signal should be proportional to
	\begin{align}\label{cs}
	S^{\mathrm{clock}} \propto f(p,\xi,k_3)\left(\frac{2k_1}{k_3}\right)^{\frac{1+p}{2(1-p)}} \mathrm{sin}\left\{ S\  \mathrm{log}\left[\left(\frac{2k_1}{k_3}\right)^{-1}\right] + \phi(p, \xi, k_3)\right\}~.
	\end{align}
	We obtain the oscillation phase
	\begin{align}\label{osci}
	S_{\mathrm{oscillation}}  = \mathrm{sin}  \left\{  S \  \mathrm{log}\left[ \left(\frac{2k_1}{k_3}\right)^{-1}\right] + \phi(p, \xi, k_3)\right\}~,
	\end{align}
	which is the essential pattern for the clock signal. We find that this oscillation pattern is the same as the inflation case and we will discuss this point later in detail at the end of Section~\ref{sec3}. It is also important to note the amplitude of the signal as a function of $k_1$, when $k_3$ is fixed. From (\ref{cs}) , the $(k_1/k_3)^{\frac{1+p}{2(1-p)}}$ terms represent how the amplitude changes with the amount of squeezeness, and the function $f(k_3)$ manifests the overall scale  dependence. Generally, $f(k_3)$ can not be determined before we specify a model.
	From the perspective of $k_3$, these two dependencies are entangled here and we are unable to distinguish them. However, the power of momentum ratio $k_1/k_3$ is determined and can be used to differentiate these scenarios. In practice, we can keep $k_3$ unchanged and increase $k_1$ to study the squeeze shape dependence.

	\subsection{The time-ordered integral}
	The outer and inner integrands of the time-ordered integral take similar forms. We rewrite (2.6) and (2.7) as
	\begin{align}
	\propto \left[\int_{-\infty}^{0} d\tau_1 c_2' a^3 v_{k_3} u_{k_3}^{'*} \int_{-\infty}^{\tau_1} d\tau_2 c_3' a^2 v_{k_3}^{*} u_{k_1}^{'*} u_{k_2}^{'*} \right.
	\end{align}
	\begin{align} \left.+\int_{-\infty}^{0} d\tau_1 c_3' a^2 v_{k_3} u_{k_1}^{'*} u_{k_2}^{'*} \int_{-\infty}^{\tau_1} d\tau_2 c_2' a^3 v_{k_3}^{*} u_{k_3}^{'*} \right]
	\end{align}
	$$+ \mathrm{c.c.} + 2 \ \mathrm{perms}~.$$

	To use the saddle point approximation, it is necessary to  make sure that both of the extreme value time $\tau_0$ are in the interval of ($-\infty, \ \tau_1$). In this case, the time-ordered integrals will share the similar oscillating pattern like (3.29). It describes the property of this clock signal, where we can identify the type of alternative scenarios.
	\\
	For simplicity, we consider $\tau_0 = -1$. The modes are denoted as
	\begin{align}
	u_k \propto \frac{1}{(-\tau)^{\frac{p}{1-p}}}  e^{- i k \tau}~,
	\end{align}
	\begin{align}
	v_k \propto \frac{1}{(-\tau)^{\frac{3p-1}{2-2p}}} \left[ C_1 e^{i S \mathrm{log}(-\tau)} + C_2 e^{- i S \mathrm{log}(-\tau)}\right]~.
	\end{align}
	We denote the variable $x_1 = -\tau_1 $ and $x_2 = - \tau_2$ and the integral (3.30) and (3.31) should be
	$$
	\propto k_1 \int_{0}^{\infty} d x_1 x_1^{\frac{1-3p}{2(1-p)}} \left[C_1^{*} e^{- i S \mathrm{ log}(x_1)} + C_2^{*} e^{ i S \mathrm{log}(x_1)}\right] e^{-2 i k_1 x_1}$$

	\begin{align}
	\times \int_{0}^{x_1} dx_2 x_2^{\frac{1+p}{2(1-p)}} \left[C_1 e^{ i S \mathrm{ log}(x_2)} + C_2 e^{ -i S \mathrm{log}(x_2)}\right] e^{- i k_3 x_2}
	\end{align}

	$$
	+ k_1 \int_{0}^{\infty} d x_1 x_1^{\frac{1-3p}{2(1-p)}} \left[C_1 e^{ i S \mathrm{ log}(x_1)} + C_2 e^{ - i S \mathrm{log}(x_1)}\right] e^{-2 i k_1 x_1}$$

	\begin{align}
	\times \int_{x_1}^{\infty} dx_2 x_2^{\frac{1+p}{2(1-p)}} \left[C_1^{*} e^{ - i S \mathrm{log}(x_2)} + C_2^{*} e^{ i S \mathrm{log}(x_2)}\right] e^{- i k_3 x_2}~.
	\end{align}
	Following the condition of the squeezed limit, we consider $k_3 = 0$ approximately in (3.34) and (3.35). Firstly we deal with the integral (3.34). Compared with the constant mass case, this integral over $x_2$ can be done directly. The second integral term is
	$$
	\left. x_2^{\frac{3-p}{2(1-p)}}\left[C_1\frac{1}{i S + \frac{3-p}{2(1-p)} } x_2^{i S}  + C_2\frac{1}{- i S + \frac{3-p}{2(1-p)} } x_2^{- i S}\right]\right|_{0}^{x_1}
	$$
	\begin{align}
	\rightarrow x_1^{\frac{3-p}{2(1-p)}}\left[C_1\frac{1}{i S + \frac{3-p}{2(1-p)} } x_1^{i S}  + C_2\frac{1}{- i S + \frac{3-p}{2(1-p)} } x_1^{- i S}\right]~.
	\end{align}
	There is a similar calculation for the second integral in (3.35).
	\begin{align}
	\left. x_2^{\frac{3-p}{2(1-p)}}\left[C_1^{*}\frac{1}{-i S + \frac{3-p}{2(1-p)} } x_2^{-i S}  + C_2^{*}\frac{1}{i S + \frac{3-p}{2(1-p)} } x_2^{ i S}\right]\right|_{x_1}^{\propto}~,
	\end{align}
	which also contains a similar  $x_1$-dependent term like (3.36).
	\begin{align}
	\rightarrow - x_1^{\frac{3-p}{2(1-p)}}\left[C_1^{*}\frac{1}{ - i S + \frac{3-p}{2(1-p)} } x_1^{-i S}  + C_2^{*}\frac{1}{ i S + \frac{3-p}{2(1-p)} } x_1^{ i S}\right]  + ... ~,
	\end{align}
	where the $\langle ... \rangle$ refers to the $x_1$-independent term from the upper infinity case. After combining with the first integral of each term, for (3.34)
	$$
	\rightarrow k_1\int_{0}^{\infty} dx_1 x_1^2 \left[C_1 \frac{1}{iS + \frac{3-p}{2(1-p)}} x_1^{i S} +
	\right.$$
	\begin{align}
	\left. C_2 \frac{1}{-iS + \frac{3-p}{2(1-p)}} x_1^{-i S}\right] \left[C_1^{*} x_1^{-i S} + C_2^{*} x_1^{i S}\right] e^{-2i k_1 x_1}~.
	\end{align}

	Only the terms with resonance remains for the contribution to the clock signal, which is proportional to
	\begin{align}
	\rightarrow \int_{0}^{\infty} dx_1 x_1^2 C_1 C_2^{*} \left(\frac{1}{iS + \frac{3-p}{2(1-p)}}\right) \mathrm{exp}\left[  2 i S\  \mathrm{log}(x_1) -  2 i k_1 x_1 \right]~.
	\end{align}

	In the same way, from (3.35)
	$$
	\rightarrow   - \int_{0}^{\infty} dx_1 x_1^2 C_1 C_2^{*} \left(\frac{1}{iS + \frac{3-p}{2(1-p)}}\right)\mathrm{exp}\left[  2 i S\  \mathrm{log}(x_1) -  2 i k_1 x_1 \right]   $$
	\begin{align}
	+ G(p , \xi) \left\{ k_1 \int_{0}^{\infty} d x_1 x_1^{\frac{1-3p}{2(1-p)}} \left[C_1 e^{ i S \mathrm{ log}(x_1)} + C_2 e^{ - i S \mathrm{log}(x_1)}\right] e^{-2 i k_1 x_1} \right\}~.
	\end{align}
	We can figure out that the oscillatory terms and coefficients of (3.39) and the first term of (3.40) are consistent with each other. So they can offset each other and only the second of (3.40) remains, which shares the same form with the non-time-ordered integral. To summarize, we can express the time-ordered integral by saddle point approximation as
	\begin{align}
	S^{\mathrm{clock}} \propto (2k_1)^{\frac{1+p}{2(1-p)}} \mathrm{sin}\left\{S \ \mathrm{log}\left[(2k_1)^{-1}\right] + \mathrm{phase} \right\}~.
	\end{align}

	\begin{figure}[hptb]
		\centering
		\includegraphics[width=0.8\textwidth]{figure.pdf}
		\caption{Squeeze shape dependence of amplitude in three different scenarios:  fast contraction ($p$=2/3) with constant mass , fast contraction ($p$=2/3) with mass $\sim H$ and exponential inflation. \label{fig2} }
	\end{figure}

	 Interestingly, this oscillation pattern is the same as the standard clock signal of inflation with constant mass.  There are two intuitive ways to understand this similarity. First of all, the clock signal is generated when the massive field oscillates as $e^{i \int m dt}$ which transformed into conformal time is $e^ {i \frac{m}{H} log(-\tau)}$ in the inflation case. This logarithmic function dependence cause the unique clock signal of inflation. However, the mass generated from Ricci scalar has the property~$m\propto t^{-1}$, this would also introduce  a logarithmic function on the exponent. Another way to understand it is from equation of motion (\ref{masseom}). The mass term combines with the scale factor as $(a m)^2$, in the inflation case, $a m \sim \tau^{-1}$ and in our case $ a m \sim a H \sim \tau^{-1}$. So that, this two different cases share similar equations of motion. As a result, the oscillation pattern of quantum clock signal becomes similar to the standard clocks for inflation.\\

	 Thus, if one uses shape information only to distinguish inflation and alternative scenarios, there is a possibility that alternative to inflation scenarios with dynamically generated mass would be confused with inflation. To break this degeneracy, we note that, although the oscillation patterns are quite similar, the amplitude of different shape functions differs greatly. As we can see from~(\ref{cs}), in addition to the oscillation part, the amplitude of this signal also shows a momentum ratio $k_1/k_3$ dependence. This $ \left({2k_1}/{k_3}\right)^{\frac{1+p}{2(1-p)}}$ term represents how the amplitude changes, when $k_3$ is fixed and one varies $k_1$. For inflation, the corresponding factor is $\sim (k_1/k_3)^{-\frac{1}{2}}$, corresponding to the $p\rightarrow \infty$ limit which differs
	 \footnote{For comparison, for alternative to inflation with constant mass, the corresponding factor is $\sim (k_1/k_3)^{-\frac{1}{2}+\frac{1}{2p}} $, which is also different.}
	 from the case of a finite $p$. We illustrate this difference in Figure~\ref{fig2}. In this non-standard case, one notes that for inflation (or super-inflation where the universe is quasi-de Sitter but with increasing energy density), $|p|>1$ and the oscillation is decreasing while $k_1$ increases. But for alternatives, $-1<p<1$ and the signal is increasing while $k_1$ increases\footnote{In standard case, for slow expansion scenarios ($-1<p<0$), the signal is increasing while $k_1$ decreases.}.

	\section{Time-dependent effective mass from nonlinear corrections} \label{sec4}
	\subsection{The effective mass}
	An effective mass of $\sigma$ may also be generated from interactions in alternative scenarios. We consider the simplest case : $V = \frac{1}{4} \lambda \sigma^4$.
	\\
	Under comparison, it can be separated as $V = \frac{1}{2} \lambda  (3 \langle\sigma^2\rangle) \sigma^2$. We can figure out that the effective mass term should be proportional to $\langle\sigma^2\rangle$, which is related to the two-point correlation function of this scalar field,
	\begin{align}
	\mu^2 = m_{\mathrm{eff}}^2 = 3 \lambda \langle\sigma^2\rangle~,
	\end{align}
	where we can estimate the time-dependent contribution of this two-point correlation in two methods \cite{Linde:2005yw}. The first method is to figure out the expression of quantum fluctuation in alternative scenarios, and do the integration in one cut-off process. In the second method, we separate the scalar in long and short wavelength part and solve them form an nonlinear stochastic different equation (SDE).

	The general EOM of scalar field $\sigma$ is
	\begin{align}
	\ddot{\sigma} + 3 H \dot{\sigma} + \frac{k^2}{a^2}\sigma + m^2 \sigma = 0~.
	\end{align}
	The last term should vanishes in this massless case. We combine the scale factor and field as $v = a \sigma$ for simplification. Shown under the conformal time $\tau$, the EOM is
	\begin{align}
	v_k'' + \left(k^2 - \frac{a''}{a} \right) v_k = 0~,
	\end{align}
	which is knowns as the Mukhanov-Sasaki (MS) equation. Here, $v_k''$ and $a''$ denote the second derivative with respect to the conformal time $\tau$.
	\\
	The scale factor $a$ is still expressed as power-law function, under these relations above,
	\begin{align}
	a =a_0 \left(\frac{\tau}{\tau_0}\right)^{\frac{p}{1-p}} \ \ \Rightarrow \ \ \frac{a''}{a} = \frac{(\frac{p}{1-p} - 1)\frac{p}{1-p}}{\tau^2}~.
	\end{align}
	So, the MS equation is
	\begin{align}
	v_k'' + \left(k^2 - \frac{\nu^2 -\frac{1}{4}}{\tau^2} \right) v_k = 0 ~,
	\end{align}
	where $\nu(p) = \frac{3}{2} + \frac{1}{p-1}$ is a model-dependent index.
	The general solution of this MS equation is a linear combination of Hankel functions,
	\begin{align}
	v_k = D_1 \sqrt{-k\tau}H_{|\nu|}^{(1)}(-k \tau) + D_2 \sqrt{-k\tau}H_{|\nu|}^{(2)}(-k \tau)~.
	\end{align}
	This solution should be normalised on the sub-Hubble scales  to constraint constants $D_1$and $D_2$. Under the limit: $- k\tau \rightarrow 0$, the quantum fluctuation $\sigma_k$ is
	\cite{Miranda:2019ara, Nakao:1988yi}
	\begin{align}
	\sigma_k = i \frac{1}{\sqrt{4 \pi k a^2}}\frac{2^{|\nu|} \Gamma(|\nu|)}{(-k\tau)^{|\nu|-\frac{1}{2}}}~.
	\end{align}
	The time-dependent contribution of quantity $\langle\sigma^2 \rangle$ is proportional to
	\begin{align}
	\int d^3 k \ \frac{1}{a^2} \ k^{-2|\nu|} (-\tau)^{1- 2|\nu|}~.
	\end{align}
	We use the time dependent physical momentum $p = \frac{k}{a}$ to emphasize the physical meaning,
	\begin{align}
	\langle \sigma^2 \rangle \propto \int_0^H dp\  p^{2-2|\nu|} \ (-\tau)^{1-2|\nu|} \ a^{1-2|\nu|}~.
	\end{align}
	Since $(-a \tau) \propto H^{-1}$ and the time dependent Hubble constant $H = \frac{\dot{a}}{a} = \frac{p}{t}$ \cite{Linde:2005ht},
	\begin{align}
	\langle \sigma^2 \rangle \propto H^{3-2|\nu|} H^{2|\nu|-1} = H^2 \propto \frac{1}{t^2}~.
	\end{align}

	There is a more accurate method to obtain the time-dependent contribution. We still consider the alternative models with the scalar field $\sigma(x, t)$.
	The idea is to separate this scalar field using the stochastic approach. We split the $\sigma$ field into the long wavelength part $\sigma_L$ and short wavelength part $\sigma_S$ with the expression
	\begin{align}
	\sigma(x, t) = \sigma_L + \sigma_S = \sigma_L + \int \frac{d^3 k }{(2 \pi)^{3/2}} \Theta[k - \epsilon a(t) H]\left[a_k \sigma_{S, k}(t) e^{-i k x} + a_k^{\dagger} \sigma_{S, k}^{*} e^{i k x}\right]~,
	\end{align}
	where $\epsilon$ is a small constant and $a_k$ and $a_k^{\dagger} $ are annihilation and creation operator. $\Theta(x)$ is the Heaviside step function. The short wavelength part satisfies the massless EOM of scalar equation (4.2) with $m^2 = 0$ so $\sigma_{S, k} = \sigma_k$ in (4.7).\\
	The long wavelength part $\sigma_L$ satisfies the classical equation of motion $\ddot{\sigma_L} + 3H \dot{\sigma_L} + \partial_i V = 0$. For the alternative scenarios with index $p$,
	\begin{align}
	\ddot \sigma_L + 3 \frac{p}{t} \dot \sigma_L + \lambda \sigma_L^3 = 0~.
	\end{align}
	We are interested in the damping dominated regime. In this special period, the damping term is much larger than the accelerating term and then we can ignore the second derivative term $\ddot{\sigma_L}$, i.e.
	\begin{align}
	\ddot \sigma_L \ll 3 H(t) \dot\sigma_L = 3 \frac{p}{t} \dot \sigma_L~,
	\end{align}
	which requires
	\begin{align}
	\lambda t^2 \ll (1-p)\frac{\sqrt{3p}}{\sigma_L}~.
	\end{align}
	Using the Starobinsky's stochastic method, the short wavelength contribution can be added to the original classical equation as a perturbation term $f(x, t)$. The quantum-corrected equation of motion is \cite{Liu:2015dda}
	\begin{align}
	3 \frac{p}{t} \dot{\sigma} = -\lambda \sigma^3 +3 \frac{p}{t} f(x, t)~.
	\end{align}
	The stochastic random force term $f(x, t)$ is
	\begin{align}
	f(x, t) = (p-1) D_1 t^{p-2} \int \frac{d^3 k}{(2\pi)^{3/2}} \delta(k - D_1 t^{p-1})\left[a_k \sigma_{S, k}(t) e^{-i k x} + a_k^{\dagger} \sigma_{S, k}^{*} e^{i k x}\right]~,
	\end{align}
	where $D_1 = \epsilon a_0 t_0^{-p} p$ is a combined constant. Here, the integration is constrained only for specific $k$ because of the delta function. $f(x, t)$ is a Gaussian random field and the two-point correlation function is
	\begin{align}
	\langle f(x_1, t_2), f(x_2, t_2) \rangle = \Lambda t^{-3} \delta(t_1 - t_2)\  j_0\left(\epsilon a(t) H|x_1 - x_2|\right)~,
	\end{align}
	where $j_0(x) = \frac{sin(x)}{x}$ and $
	\Lambda$ is a time-independent combined coefficient \cite{Starobinsky:1994bd}.
	\\
	The quantum-corrected equation of motion then becomes one nonlinear stochastic differential equation (SDE)
	\begin{align}
	\dot{\sigma} = - \frac{\lambda}{3p} t \sigma^3 + \frac{\sqrt{\Lambda}}{3p} t^{-\frac{3}{2}} \eta(x, t)~,
	\end{align}
	where $\eta(x, t)$ is the simplified function with $\langle \eta(x, t) \rangle = 0 $ and $\langle\eta(x_1, t_1),  \\ \eta(x_2, t_2)\rangle= \delta(t_1 - t_2) \delta(|x_1 - x_2|)$. Because of the time and field-dependent drift coefficient $-\frac{\lambda}{3p} t \sigma^3 $ and time-dependent diffusion coefficient $\frac{\Lambda}{18 p^2} t^{-3}$, we cannot figure out the analytic solution of this nonlinear SDE. The numerical solution shows that the proportion to $t^{-2}$ is still an appropriate approximation for the two-correlation function $\langle \sigma^2 \rangle$. \\
	In conclusion, the effective mass in this case is expressed as
	\begin{align}
	\mu^2 = m_{\mathrm{eff}}^2 \propto \frac{1}{t^2}~.
	\end{align}
	And the effective mass and the potential term become
	\begin{align}
	\mu^2 = 2 \frac{C(p)}{t^2},\ \
	V = \frac{C(p)}{t^2} \sigma^2~,
	\end{align}
	where $C(p)$ is a time-independent coefficient which is model-dependent. Approximately, by the first method,
	\begin{align}
	C(p) = 3\lambda \frac{\Gamma^2(|\nu|) \ 2^{2|\nu|}}{64 \pi^4}~,
	\end{align}
	for the interacting coefficient $\lambda > 0$, $C(p)$ and the potential are always non-negative, which is different from the Ricci-dominated case. Note that there is an undefined scenario for $p = \frac{1}{3}$ ($\nu = 0$). This is the only case leading to an infinite Gamma function so this contracting scenario cannot be dealt with in this way.

	\subsection{The clock signal}
	Since the effective mass is proportional to $t^{-2}$, the clock signal dominated by the quantum fluctuation should be similar to the Ricci-dominated case. Like (3.6), the conformal time basis EOM of scalar field mode $v_k$ is
	\begin{align}
	\frac{d^2 v_k}{d \tau^2} + \frac{2p}{(1-p)\tau}\frac{d v_k}{d \tau} + \frac{2 C(p)}{(1-p)^2 \tau^2} = 0~.
	\end{align}
	The general solution is
	\begin{align}
	v_k = (-\tau)^{\frac{1-3p}{2-2p}}\left[e^{i B(p) log(-\tau)}C_1 + e^{-i B(p) log(-\tau)}C_2\right]~,
	\end{align}
	\begin{align}
	B(p) =  \frac{\sqrt{8 C(p) - (1- 3p)^2}}{2(p-1)}~,
	\end{align}
	which has the same form as (3.15). There is also an restriction on $p$, like the discussion in the last section since $B(p)$ must be real. In the same method like (3.28), we can figure out the clock signal in this case should be proportional to
	\begin{align}
	S^{\mathrm{clock}} \propto (2k_1)^{\frac{1+p}{2(1-p)}} \mathrm{sin}\left\{ B(p)\ \mathrm{log}\left[ \left(2 k_1\right)^{-1}\right] + \mathrm{phase} \right\}~,
	\end{align}
	where C($p$) follows (4.20) expression with $\nu = \frac{3}{2}+ \frac{1}{p-1}$.

	\section{Conclusion} \label{con}
	In this paper, we extend the study of quantum primordial non-standard clocks to alternative scenarios with dynamically generated mass. Such time-dependent mass can naturally be generated where the background significantly break scale invariance. Two mechanisms are considered:

	The first mechanism is through non-minimal coupling with Ricci scalar $R$ which should be a constant ($\propto H^2$) in de-sitter space-time, but it can contribute a time-dependent effective mass in different alternatives to inflation scenarios with $t^{-2}$ time dependence. \\

	We note that not all alternatives to inflation scenarios can produce non-trivial quantum primordial non-standard clocks signal from coupling to $R$. For generating oscillatory signals, the mode function of massive fields should have oscillation behaviors, this condition places a constrain on the power-law index $p$ as a function of $\xi$, as plot in Figure~\ref{fig1}. \\

	The second mechanism of dynamical mass generation is from quantum loop correction, we give a simple approximation of this method's contribution. For the  massless field with $\lambda \sigma^4$ interaction, we show that the time dependence of effective mass is also proportional to $ H^2$. \\

	Finally, the oscillation behavior of this situation is quite similar to inflation scenarios with the time-independent mass case, because massive fields in these two different scenarios share the similar equation of motion. However, we can still distinguish them from the shape dependence of the amplitude. The amplitude of shape function in our case as  $(k_1/k_3)^{\frac{1+p}{2(1-p)}}$ when $k_1$ varies, which is a decreasing function for inflation and an increasing function for alternative scenarios. It is interesting to see if similar observations can be used to distinguish classical standard and non-standard primordial clocks.

	\section*{Acknowledgement}
	We thank Xingang Chen and Siyi Zhou for fruitful discussions and comments. This work was supported in part by ECS Grant 26300316 and GRF Grant 16301917 and 16304418 from the Research Grants Council of Hong Kong.

redpajama_set_name: RedPajamaArXiv


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Trying out a different perspective on the karma toady. Just a quick edit to really shows how much the gimbal works hard for us.
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text:
Q: Beamer buttons in article I want to produce the same result as this commands related to the beamer-class in a document using the article-class :
\hyperlink{question}{\beamergotobutton{Allez à la question}}
\hyperlink{partie}{\beamerskipbutton{Sautez cette partie}}
\hyperlink{label}{\beamerreturnbutton{Retour}}

This produces the following output :

Is there a way to have the same output in an article ?
For some context, I want to use this buttons to link pages and text segments across a document with hyperlinks that I can already produce with hyperref.

A: You can achieve something simiar using a customized tcolorbox:

\documentclass{article}
\usepackage{amssymb}

\usepackage[most]{tcolorbox}

\definecolor{myblue}{RGB}{153,153,217}
\newtcbox{\inlinebox}[1][]{enhanced,
                           box align=base,
                           nobeforeafter,
                           colback=myblue,
                           size=small,
                           boxrule=0pt,
                           left=0pt, right=0pt,
                           boxsep=2pt,
                           arc=5pt,
                           fontupper=\color{white},
                           #1}

\newcommand{\mylinkbox}[1]{\inlinebox{$\blacktriangleright$  \nameref{#1}}}

\usepackage{nameref}
\usepackage[hidelinks]{hyperref}

\begin{document}
\section{first section}\label{sec:example}
\newpage
Some regular text and a link box: \mylinkbox{sec:example} more regular text
\end{document}

A: Just for fun. I pick "button" related definitions from beamer source files and replace \(def|use)beamertemplate staff by some direct macro uses.
Beamer hard-coded the size of the rounded rectangle (for example, try replace \tiny with \small in example below), so for a more flexible (but less efficient) solution, a tikz node with shape rounded rectangle is better.
\documentclass{article}
\usepackage{tikz}
\usepackage{hyperref}

% copied from beamercolorthemedefault.sty
% begin
\definecolor{beamer@blendedblue}{rgb}{0.2,0.2,0.7}
% end

\colorlet{button}{beamer@blendedblue}
\colorlet{button border}{beamer@blendedblue}

\makeatletter
\newbox\beamer@tempbox
\newdimen\beamer@tempdim

% copied from beamerinnerthemedefault.sty
% begin
\newdimen\beamer@dima
\newdimen\beamer@dimb

%\defbeamertemplate*{button}{default}
\def\beamer@@tmpl@button
{%
  \setbox\beamer@tempbox=\hbox{{\insertbuttontext}}%
  \ht\beamer@tempbox=6pt%
  \dp\beamer@tempbox=0pt%
  \setbox\beamer@tempbox=\vbox{\box\beamer@tempbox\vskip2pt}%
  \beamer@tempdim=\wd\beamer@tempbox%
  \beamer@dima=\beamer@tempdim\advance\beamer@dima by2.2pt
  \beamer@dimb=\beamer@tempdim\advance\beamer@dimb by4pt
  \begin{pgfpicture}{-4pt}{0pt}{\the\beamer@tempdim}{8pt}
%    \color{bg}
    \pgfsetfillcolor{button}
    \pgfsetlinewidth{0.8pt}
    \pgfpathqmoveto{0pt}{0pt}
    \pgfpathqcurveto{-2.2pt}{0pt}{-4pt}{1.8pt}{-4pt}{4pt}
    \pgfpathqcurveto{-4pt}{6.2pt}{-2.2pt}{8pt}{0pt}{8pt}
    \pgfpathlineto{\pgfpoint{\the\beamer@tempdim}{8pt}}
    \pgfpathcurveto%
    {\pgfpoint{\the\beamer@dima}{8pt}}%
    {\pgfpoint{\the\beamer@dimb}{6.2pt}}%
    {\pgfpoint{\the\beamer@dimb}{4pt}}
    \pgfpathcurveto%
    {\pgfpoint{\the\beamer@dimb}{1.8pt}}%
    {\pgfpoint{\the\beamer@dima}{0pt}}%
    {\pgfpoint{\the\beamer@tempdim}{0pt}}
    \pgfpathclose
    \pgfusepathqfill
%    \colorlet{bg}{parent.bg}
%    \usebeamercolor[fg]{button border}
    \pgfsetstrokecolor{button border}
    \pgfpathqmoveto{0pt}{0pt}
    \pgfpathqcurveto{-2.2pt}{0pt}{-4pt}{1.8pt}{-4pt}{4pt}
    \pgfpathqcurveto{-4pt}{6.2pt}{-2.2pt}{8pt}{0pt}{8pt}
    \pgfpathlineto{\pgfpoint{\the\beamer@tempdim}{8pt}}
    \pgfpathcurveto%
    {\pgfpoint{\the\beamer@dima}{8pt}}%
    {\pgfpoint{\the\beamer@dimb}{6.2pt}}%
    {\pgfpoint{\the\beamer@dimb}{4pt}}
    \pgfpathcurveto%
    {\pgfpoint{\the\beamer@dimb}{1.8pt}}%
    {\pgfpoint{\the\beamer@dima}{0pt}}%
    {\pgfpoint{\the\beamer@tempdim}{0pt}}
    \pgfpathclose
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redpajama_set_name: RedPajamaStackExchange


LENEXA, KAN. – Jack Lucks has an "architectural eye." His dedication to creating attention-grabbing projects has served him well during the past 43 years as he makes design and product decisions related to a variety of projects with different architectural styles.
In recent years Lucks and his group, Continental Real Estate Companies, have focused on the creation of senior/assisted living facilities. Projects are underway in Pittsburgh, Pa., Columbus, Ohio and Lexington, Ky. A recently-opened Middleton facility in Granville, Ohio has been well received.
"When I find a building product that looks good with a project I try to stick with it," says Lucks, founding partner at Continental Real Estate Companies. "That's been the case with the synthetic slate roofing we selected for the Granville project. The black Bellaforté Slate roof from DaVinci Roofscapes has the aesthetic look we wanted without the weight of real slate.
Middleton is situated near the quaint village of Granville that is home to Denison University. Closely located to historic shops and restaurants, Middleton provides residents with options for enjoying a relaxed lifestyle.
With 94 rooms, Middleton offers a caring environment for retirees. Six levels of support are available at the 92,000 square foot structure, allowing residents to remain in the facility long-term. Restaurant-style dining, daily activities, an on-site theatre and walking nature paths make life enjoyable for residents of the community. For their personal needs, laundry and housekeeping services, 24-hour licensed nurses and a beauty salon are available.
For more details on the expansive services offered by Continental Real Estate Companies.


text:
Say His Name: Ahmad al Alawi Alissa
Earlier: Immigrant Mass Murderer Ahmad Al Aliwi Al-Issa Kills 10 White Americans—Regime Media Says It's About Guns
Here are two interesting examples of how the New York Times covers mass murderers when they aren't dread white males.
From the New York Times news section:
The Mystery of Why a Foundering Football Player Killed a Family
A small city that bills itself as Football City U.S.A. is grappling with the shooting deaths of members of a prominent local family by Phillip Adams who, many say, had been adrift after his N.F.L. career ended.
By Jonathan Abrams, Ken Belson and John Jeter
He struggled to find work. His last-ditch chance to make an N.F.L. team fizzled. He had a child to support and little apparent direction in a life freighted with high expectations. His behavior was increasingly erratic. Then on Wednesday, for reasons no one yet knows for sure, Phillip Adams, a former N.F.L. cornerback, went to the Rock Hill, S.C., home of a prominent doctor and shot everybody he saw before fatally turning the gun on himself.
Now, the football-loving community of 65,000 that bills itself as Football City U.S.A. is struggling to contend with Adams's suddenly violent turn and its aftermath.
Before he killed five people, including two children, and critically wounded a sixth person,
The cornerback's six victims were all white, but who is counting?
Adams, 32, who shot and killed himself several hours after his rampage, had seemed adrift since he last played N.F.L. football almost six years ago, friends and associates said. He remained close to home, caring for his mother, Phyllis, a former high school teacher who became a paraplegic after a car accident a decade ago.
This story sounds rather like the Black Muslim ex-college football player who went crazy and murdered the white Capitol cop last week. Like I wondered then: lots of people go nuts or break down, especially black males, but is the Racial Reckoning making them more murderous?
Meanwhile, the NYT runs an article about the victims in Boulder of the Muslim immigrant terrorist. But this article refuses to even mention the shooter's glaringly Arabic name.
'I Know She's Gone, but Why?': Love and Loss at a Boulder Grocery Store
Funerals for the victims of the mass shooting in Colorado were being held this week. Teri Leiker, a beloved employee at the King Soopers store for 31 years, was among them.
By Jack Healy
BOULDER, Colo. — Teri Leiker and Clint Ponsford shared a love story that began and ended at the grocery store.
They spent more than 30 years working at the same King Soopers supermarket in Boulder, where Ms. Leiker charmed customers with her big laugh and Mr. Ponsford could spot the peaks of the Flatirons when he went outside to wrangle shopping carts. They had both competed in Colorado's Special Olympics and helped each other get through a lot: deaths, a breakup and the challenges of navigating this world as two people with cognitive disabilities.
About a year and a half ago, their friendship turned into something deeper. They went on karaoke dates. They watched Disney movies that Ms. Leiker adored. On workdays, they would get up at 3:30 a.m. in Ms. Leiker's condo to make coffee, trade kisses and watch reruns of "Murder, She Wrote" before Mr. Ponsford left for the early shift.
And on March 22, they were both at work when it was all blasted apart.
For a few fleeting days, the country's horrified gaze was fixed on Boulder after Ms. Leiker, 51, and nine other people at the King Soopers were killed by a 21-year-old gunman whose motives remain a mystery.
But that's it: the entire article doesn't mention the identity of the shooter.
Say his name: Ahmad Al Alawi Alissa.
[Comment at Unz.com]
Steve Sailer April Fundraiser at Unz.com.
Make (tax-deductible) donations earmarked for Steve Sailer here.
Please don't forget to click Steve's name so the money goes to him: first, click on "Earmark your donation," then click on "Steve Sailer."

redpajama_set_name: RedPajamaCommonCrawl


The pollination of California's almonds is the largest annual managed pollination event in the world, with close to one million hives (nearly half of all beehives in the US) being trucked in February to the almond groves. Much of the pollination is managed by pollination brokers, who contract with migratory beekeepers from at least 49 states for the event. This business has been heavily affected by colony collapse disorder, causing nationwide shortages of honey bees and increasing the price of insect pollination. To partially protect almond growers from the rising cost of insect pollination, researchers at the Agricultural Research Service (ARS) have developed a new line of self-pollinating almond trees. Self-pollinating almond trees, such as the 'Tuono', have been around for a while, but their harvest is not as desirable as the insect-pollinated California 'Nonpareil' almond tree. The 'Nonpareil' tree produces large, smooth almonds and offers 60–65% edible kernel per nut. The 'Tuono' has thicker, hairier shells and offers only 32% of edible kernel per nut, but having a thick shell has advantages. The 'Tuono's' shell protects the nut from threatening pests such as the navel orangeworm. ARS researchers have managed to crossbreed the pest-resistant 'Tuono' tree with the 'Nonpareil', resulting in hybridized cultivars of almond trees that are self-pollinated and maintain a high nut quality. The new, self-pollinating hybrids possess quality skin color, flavor, and oil content, and reduce almond growers' dependency on insect pollination.
The seeds of Prunus dulcis var. dulcis are predominantly sweet both aspects making this trait easier to domesticate. The fruits from Prunus dulcis var. amara are always bitter, as are the kernels from other Prunus species, such as peach and cherry (to a lesser extent).
The almond is a nutritionally dense food and a 100 gram serving is a rich source (>20% of the Daily value, DV) of the B vitamins riboflavin and niacin, vitamin E, and the essential minerals calcium, iron, magnesium, manganese, phosphorus, and zinc. The same serving size is also a good source (10–19% DV) of the B vitamins thiamine, vitamin B6, and folate; choline; and the essential mineral potassium. They are also rich in dietary fiber, monounsaturated fats, and polyunsaturated fats, fats which potentially may lower LDL cholesterol. Typical of nuts and seeds, almonds also contain phytosterols such as beta-sitosterol, stigmasterol, campesterol, sitostanol, and campestanol, which have been associated with cholesterol-lowering properties.
Similarly, Christian symbolism often uses almond branches as a symbol of the Virgin Birth of Jesus; paintings and icons often include almond-shaped haloes encircling the Christ Child and as a symbol of Mary. The word "Luz", which appears in Genesis 30:37, sometimes translated as "hazel", may actually be derived from the Aramaic name for almond (Luz), and is translated as such in some Bible versions such as the NIV. The Arabic name for almond is "laoz". In some parts of the Levant and North Africa it is pronounced "loz", which is very close to its Aramaic origin.
Almond Facts for Kids. Kiddle Encyclopedia.


Not Quite Out of the Woods, from the cycling company Kitsbow, has it all: back-door adventures, amazing parenting, and, of course, bikes. The Maynard family lives in western Massachusetts, with gnarly technical mountain-bike terrain just outside their home. The film chronicles five-year-old Eleanor's battle with leukemia and how that impacts the family's relationship with the outdoors.


In My Elyment (IME) is an elite event planning company that has been serving the wedding community since 2011. The lead event designer, Sholla, has over 18 years of Project Management experience and is a Certified Coordinator with the Wedding Planner Institute of Canada. Sholla is a certified Sandals Specialist, Sandals WeddingMoons Specialist, Barbados Specialist and Mexico Destination Wedding Specialist, so she can help you plan that destination wedding you've always dreamed of!


The CGIAR Research Program on Livestock (Livestock CRP) recently announced with pleasure the appointment of Dr. Isabelle Baltenweck as its new flagship leader for Livestock, Livelihoods and Agro-food Systems (LLAFS). Originally from France, Isabelle brings to the role close to 20 years of post-doctoral experience in smallholder value chains in Africa, South and South-East Asia, with a focus on livestock farming. She has played a central role in the flagship through its different iterations, first as the Livestock & Fish CRP and in its current form, as the Livestock CRP.
On International Women and Girl's in Science day, we celebrate Isabelle's contributions as an agricultural economist with the International Livestock Research Institute (ILRI) for 19 years, while looking ahead to her new role that she is inheriting from Dr. Steve Staal, where she will draw upon her varied areas of expertise in farm level economics, value chains, gender, livelihoods and systems approach.
Here Isabelle shares with us her vision for the LLAFS flagship and talks about what motivates her most.
Quite a lot of work has been accomplished in the first phase of the CRP as Livestock and Fish, and now two years into the current phase, we have a real chance now to consolidate research outputs in order to generate some solid international public goods, through applying lessons learned from our cross country and cross commodity experiences.
We are able now to formulate fewer and more focused research questions – including whether livestock can really help move farming communities onto the path towards gender equity. We are also in a position to concretely inform the debate on how and why it is important to invest in livestock value chains, for which types of benefits, and at various levels – i.e. farm, value chain and country.
I believe in inter-disciplinary work, and for me this is what the Livestock CRP is all about – harnessing the expertise of different people. I enjoy working with people from different disciplines and being challenged. I also know livestock systems well, especially dairy.
Mostly, I want to ensure is that our research answers important questions, not just the ones from donors, but especially those from the livestock communities and stakeholders that we serve.
We need to be looking at how the research conducted in different countries are answering the CRP's research questions, helping us to identify innovations that can have the most impact. For example, what are better ways for farmers to access the needed inputs and services – those that enable value chain actors to be more profitable and improve their livelihoods. We need to provide evidence on various options so that people–from an animal health provider, a woman livestock trader, to an extension or ministry person–can make an informed choice, taking into account trade-offs.
What drew you towards working as an agricultural economist in agricultural research for development?
I believe scientists, including economists, have a responsibility to make the world a better place.
I could have been a farmer (though I'm way too risk averse) or a development practitioner (but I spend too much time considering different options), so I ended up in research. Economics is about looking at options and trade-offs, and this approach allows us to better understand decision making and processes.
What are some of your professional highlights?
I would say the contribution I made to the Heifer-led East Africa Dairy Development project. ILRI was the research partner and I contributed to the design and implementation of this multi-country, multi-partner project. Being able to influence the design of the 2nd phase was a great achievement, moving it away from a "one-size-fits-all" hub model to a flexible hub approach.
I also take great pride in seeing my various staff and students increase their capacity – capacity strengthening is a big part of what I do (not only formal training).
It would have to be working with great colleagues, and knowing that I will learn something new (almost) every day.


Monday thru Friday from 8am to 5pm.
Bonaire Workspaces is the first provider on Bonaire of all-inclusive office spaces with the highest standards.
With all the necessary office facilities included, everyone can start working right away! Organizing a meeting or event is easy with the extra space available. Fast internet and wifi connections are standard. Any rental period is possible: a day, a week or multiple months / years are no problem. Stop by and take a look….
Fast internet and wifi connections are standard. Any rental period is possible: a day, a week or multiple months / years are no problem. Stop by and take a look….


text:
Q: enhanced config parser for python 2.7 i am using configparser in python 2.7.  it lacks some key features which i need, so i am wondering if there is an alternative.
here are some features which i am looking for:

*

*case sensitivity for sections and options

*ability to reference options from different sections.  example:
[foo]
a = 1

[bar]
b = <foo::a>

bar::b would be 1

*ability to include other files inline.  example
my_include.ini
[foo]
bar = 1

main.ini
    [hello]
    a = 1

    include my_include.ini
    [bye]
    b = <foo::bar>

bye::b would evaluate to 1

*ability to include files with variables in path.  example:

my_include1.ini
    [hi]
    a = 5

main.ini
    [foo]
    bar = 1

    # this would load my_include1.ini
    include my_include<foo::bar>.ini

*ability to access debug info.  example, it can print which line of which file defined a variable.

anything out there with some/all of the above features?
thanks!


Powered by sensational 14-year-old Alex Eala, the Philippines qualified for the first the time in 26 years to the ITF World Junior Championships for girls 14-under after beating Hong Kong, 2-0, Thursday in Kuala Lumpur.
The Filipinas, also composed of Alexa Joy Milliam and Jen Prulla, will compete in the 16-nation Worlds in August in Czech Republic.
They beat Sri Lanka in the opening round before defeating Indonesia to make the quarterfinals. Last Wednesday, the Philippines also bested New Zealand.
The Philippines, coached by former nations player Czarina Mae Arevalo, last made it to the Worlds in 1993.


Outer Banks Clam Bakes are a fun and interactive meal that your family gets to enjoy local OBX seafood.
Most vacationers are used to a traditional, New England Clambake – a clam bake was an all day affair with pits dug filled with hot rocks & seaweed. Ten O Six Catering has developed a more contemporary style clambake!
An Outer Banks' clambake is perfect for large outdoor parties but can also be lots of fun at your vacation rental home, or office party. For parties of 25 to over 250 people, a clam bake is fun, delicious and a great way to celebrate summer or any special occasion.
Clambakes aren't just clams, they feature shrimp, blue crabs, corn on the cob, rolls, homemade salads, drawn butter, bibs, and more. We come, set up while you sit back and enjoy!
Crab stuffed mushrooms, Homemade Tomato & Basil Bruschetta, Stuffed Clams.
Shrimp, clams, mussels, andouille sausage, corn on the cob and red potatoes; all steamed with our house seafood spice mix.
Based out of Kill Devil Hills, NC, Ten O Six Catering provides services from Carova (4×4 area) and all towns throughout the OBX all the way south to Hatteras Village.
We will travel to other parts for the right group.
Ten O Six Clambakes are quickly becoming a bride's favorite for their special day dinner!!!
Check out our clambake menu or give us a call @ 252-261-5817 or Contact Us to customize your menu for your event!!!


text:
New%201%25%20Excise%20Tax%20on%20Stock%20Buybacks%20May%20Have%20Far-Reaching%20Consequences%20for%20Capital%20Markets%2C%20SPAC%20and%20M%26A%20Transactions
https://www.whitecase.com/insight-alert/new-1-excise-tax-stock-buybacks-may-have-far-reaching-consequences-capital-markets
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New 1% Excise Tax on Stock Buybacks May Have Far-Reaching Consequences for Capital Markets, SPAC and M&A Transactions
Scott Fryman |
Colin J. Diamond |
Neil Clausen
On August 16, 2022, President Biden signed into law the Inflation Reduction Act of 2022, H.R. 5376 (the "Act"), a reconciliation bill that revives parts of the tax legislation from the ill-fated Build Back Better Act as part of a larger package also addressing climate change, energy and health care. In particular, the Act establishes a new one-percent excise tax on certain stock buybacks by domestic public companies (the "Excise Tax"). As discussed below, the Excise Tax has a broad reach that could unexpectedly affect a range of capital markets, SPAC and M&A transactions beyond plain vanilla stock buybacks.
The statutory language implementing the Excise Tax is identical to that of the excise tax proposed at the end of 2021 as part of the Build Back Better Act. The purported policy goals of the Excise Tax are to raise revenue1 for other legislative initiatives, encourage reinvestment by public companies of funds that otherwise might be earmarked for a buyback, and to curb stock buybacks, which proponents of the tax argue inappropriately enrich corporate executives and wealthy shareholders and enable tax avoidance.2 The tax avoidance argument ostensibly relates to the fact that a typical buyback of appreciated stock by a public company (as opposed to a typical dividend) allows holders to reduce taxable income by the cost basis in the repurchased shares.
The Excise Tax was not part of the Senate's original bill of the Act, and was added as a compromise reached with Senator Krysten Sinema, D-Arizona, that included dropping the proposal to extend the holding period for carried interest payable to private equity fund managers to qualify as long-term capital gains.
Scope of the Excise Tax
The Excise Tax generally consists of a non-deductible one-percent tax on the value of stock of a "covered corporation" that is either repurchased by, or acquired by certain affiliates of, such covered corporation during a taxable year. The statute applies to buybacks taking place after December 31, 2022 and does not provide any "grandfathering rule" for repurchases pre-authorized on or prior to such date (for example, pursuant to a Rule 10b5-1 plan).
A "covered corporation" is a domestic corporation (or certain non-US corporations treated for tax purposes as a domestic corporation under the "inversion" rules) the stock of which is traded on an "established securities market."3 In limited circumstances, acquisitions of stock of certain publicly traded non-domestic corporations by their domestic subsidiaries will be treated as repurchases subject to the Excise Tax.
The value of stock treated as repurchased during the taxable year for purposes of computing the Excise Tax is reduced by the value of any new issuances of stock by the corporation during the same taxable year (the "Netting Rule").
The statute defines "repurchase" broadly by reference to Section 317(b) of the Internal Revenue Code of 1986, as amended (the "Code"), which generally includes any acquisition of stock by the corporation in exchange for cash or property other than the corporation's own stock or stock rights. The Excise Tax further expands this definition by including any other "economically similar" transaction, as determined by Treasury.
The Act excludes the following repurchases from the Excise Tax:
To the extent the repurchase is part of a tax-free reorganization under Section 368(a) of the Code, and no gain or loss is recognized by the shareholder by reason of the reorganization.
The repurchased stock, or an amount of stock equal to the value of such repurchased stock, is contributed to an employer-sponsored retirement plan, employee stock ownership plan, or similar plan.
The total amount of repurchases within the taxable year does not exceed $1 million.
Under regulations prescribed by Treasury, the repurchase is by a dealer in securities in the ordinary course of business.
The repurchase is by a regulated investment company or a real estate investment trust.
To the extent the repurchase is treated as a "dividend" (as opposed to being treated as a "sale or exchange") for US federal income tax purposes.
In addition, the statute explicitly authorizes Treasury to prescribe regulations and other guidance as are necessary to carry out, and to prevent avoidance of the Excise Tax, including to address special classes of stock and preferred stock.
These exclusions make sense when viewed in light of the purported policy objectives of the Excise Tax. For example, distributions treated as a dividends for tax purposes were presumably excluded due to the view that dividends do not present the same tax avoidance concerns.
Nevertheless, the statute leaves open a number of questions as to its intended scope. The policy objectives of subjecting corporations to the Excise Tax in connection with several of the transactions discussed below are not readily apparent. Guidance from Treasury clarifying ambiguities in the statute and excluding from the statute's reach transactions the taxing of which do not further the statute's stated policy goals will be important to clear implementation.
Observations and Open Questions
"Repurchases" of "Stock"
The Excise Tax applies broadly to repurchases of all types of stock of a covered corporation. The statute's broad applicability seemingly brings within its reach repurchases of non-traded stock acquired in privately negotiated transactions, and stock that is puttable by the holder, callable by the issuer or mandatorily redeemable pursuant to its terms (such as mandatorily redeemable preferred stock), even if such stock was issued prior to January 1, 2023.
Repurchases of other instruments that do not constitute equity securities for corporate purposes, but are treated as stock for applicable tax purpose, such as penny warrants, could also trigger the Excise Tax.
An issuer of convertible debt might repurchase shares of its own stock ahead of or concurrently with the issuance of convertible debt to limit the dilutive impact of the potential conversion of the debt. The repurchase would be subject to the Excise Tax without an offset to the amount repurchased under the Netting Rule unless the debt is converted into stock in the same taxable year.
The Excise Tax could also affect equity hedging transactions commonly entered into by companies in connection with their convertible debt issuances. Issuers of convertible debt often enter into either a capped call or a bond hedge with a warrant to mitigate the potential share dilution and offset cash outlays associated with the debt conversions. Upon conversion, these hedge transactions allow issuers to buy back shares from hedging counterparties at pre determined prices (i.e., physically settle the transaction) or, in the alternative, cash settle the hedging transaction by obtaining the upside entirely in cash or net share settle the transaction by only obtaining an amount of shares representing the upside.
In the case of a physical settlement or a net share settlement of such hedging transaction, the issuer will receive its own shares at a below-market price, and therefore the Excise Tax could apply. It is not clear, however, if and to what extent the Excise Tax and/or the Netting Rule would apply to net cash settlements of such hedging transactions or convertible debt. For instance, further guidance might clarify that in circumstances (such as a cash settlement of these hedging transactions) where a cash payment could be considered the economic equivalent of a series of transactions involving a repurchase followed by an issuance (or vice versa), the Excise Tax will apply in the same manner as it would have to such equivalent transactions when viewed together.
Because there is no grandfathering for existing transactions, companies that currently have these hedging transactions should pay particularly close attention to the Excise Tax, especially when selecting the method of settlement.
Another type of transaction that may be subject to the Excise Tax is an accelerated share repurchase ("ASR"). In an ASR, a company enters into a forward transaction with a dealer under which in exchange for a prepayment amount (which corresponds to the amount the company is committing to spend on repurchasing its shares), the company receives a number of shares usually representing approximately 80% of the total shares it could repurchase based on the then-current price. The dealer typically would have borrowed the shares it delivered to the company, and would enter into open market transactions to purchase the company's shares and close out its borrowed positions throughout the term of the ASR. The final price per share of the company's repurchase under an ASR is generally the mean of the volume-weighted average price of the shares over the term of the transaction. Depending on the final price per share, the dealer would deliver more shares to the company at the final settlement or the company may have to return some shares or cash to the dealer (e.g., if the final price is higher than the share price at the prepayment date).
An ASR is a repurchase of the company's own shares to which the Excise Tax is expected to apply. However, it is unclear if the Excise Tax would apply at the initial prepayment date (i.e., when the company first receives the majority of its purchased shares) or the final settlement date (i.e., when the final price of the repurchase is determined). This delineation is of particular importance to ASRs entered into this year with a final settlement date that occurs on or after January 1, 2023, the date on which the Excise Tax goes into effect. Similar to the point discussed above with respect to convertible notes and corresponding hedging transactions, it is not clear how and/or to what extent the Excise Tax and/or Netting Rule would apply to cash settlements of an ASR.
Employee Plans and Anti-Dilution Buybacks
Many companies use stock buyback programs to manage the dilutive effect of stock issued to (or for the benefit of) employees through retirement plan contributions, such as 401(k) plan matching contributions, or to satisfy awards under incentive compensation plans (e.g., stock options and RSUs). While the Act includes an exception for repurchases intended to offset contributions to "an employer-sponsored retirement plan, employee stock ownership plan, or similar plan," the scope of this exception is uncertain absent more guidance from Treasury.
For example, the term employee stock ownership plan, or ESOP, is usually understood to mean a specific type of tax-qualified retirement plan funded by employer stock, and not a stock option plan or employee stock purchase plan (ESPP). It is also unclear whether an employer-sponsored retirement plan would only cover broad-based retirement plans such as pensions and 401(k) plans, or also so-called "top hat" deferred compensation plans that by design may only benefit a select group of highly compensated employees. Given the policy goals offered by proponents of the Excise Tax noted above, it is notable that pension plans, 401(k) plans and ESOPs are all subject to the Employee Retirement Income Security Act (ERISA), a federal law established to protect employees, while top-hat plans and typical equity incentive plans are not covered by ERISA and may disproportionately benefit senior executives.
The Excise Tax could also have unexpected application to domestic-incorporated special purpose acquisition companies ("SPACs"). In particular, absent guidance from Treasury providing otherwise, redemptions of public A shares in connection with a business combination would be subject to the Excise Tax even though the repurchases are pursuant to the terms of the stock and notwithstanding the fact that the redeemed shareholders might not be realizing any gain on the repurchases. The Excise Tax can also apply where shareholders opt to have their shares redeemed in connection with specified material amendments to SPAC charters to extend investment periods.
The Netting Rule could provide relief in many cases involving domestic-incorporated SPACs where the value of shares issued to shareholders of the target company and PIPE investors in a business combination exceeds the value of shares redeemed, or if the business combination closes in the same year as the IPO. The Netting Rule might be of limited utility, however, where the target shareholders do not roll over into the existing SPAC entity, such as in "up-C," "double dummy" or "target-on-top" structures. It remains to be seen whether Treasury will offer relief in these instances by, for example, expanding the Netting Rule to include issuances by a successor to a covered corporation (such as the new holding company in certain "double dummy" structures), certain exchange rights or options to acquire covered corporation stock (such as in "up-C" structures), or deemed issuances of retained equity in "target-on-top" structures.
Given the broad definition of "repurchase" in the statute, and Treasury's authority to cause transactions economically similar to a repurchase to be treated as such, a distribution of property in whole or partial dissolution or liquidation of a covered corporation may be subject to the Excise Tax. This outcome would be particularly onerous for domestic SPACs, as SPACs are generally required to liquidate if they do not consummate a business combination within a pre-determined period (typically 18 to 24 months, unless an extension is approved).
The potential application of the Excise Tax could provide additional incentives to form SPACs in the Cayman Islands. If a Cayman-domiciled SPAC, however, identifies a domestic target and, as is typically the case, migrates to the United States to effect the business combination, it is not clear whether such SPAC would nonetheless be subject to the Excise Tax if it redeems Class A shares after the migration. It also remains to be seen whether the SPAC could avoid the tax by repurchasing shares prior to the domestication.
Other M&A Transactions
Several other types of transactions that appear not to involve a repurchase in form, but nonetheless constitute a "redemption" under Section 317(b) of the Code could also result in unexpected application of the Excise Tax. For example, where a covered corporation is acquired with transaction consideration funded in part from cash on the covered corporation's balance sheet and/or debt proceeds borrowed (or treated as borrowed) by the covered corporation, such transaction consideration would generally be treated as paid to the shareholders in redemption of their stock for income tax purposes.
Similarly, in partially tax-free reorganizations where a covered corporation is acquired by another corporation for at least the requisite minimum stock consideration to qualify for tax deferral and taxable cash "boot," it is possible that all or a portion of the cash consideration would be treated as paid to shareholders in redemption of their shares for income tax purposes. It is also not entirely clear on the face of the statute whether the stock component of the consideration in such transactions (which is generally permitted to be received on a tax-deferred basis) would trigger the Excise Tax, because the statutory exclusion only exempts repurchases that are part of a tax-free reorganization where no gain or loss is recognized.
A type of tax-deferred reorganization known as a "split-off" could also trigger the Excise Tax under the statute. A split-off involves an exchange (treated as a redemption for income tax purposes) by certain shareholders of their stock in a corporation for stock of the corporation's corporate subsidiary in a transaction that otherwise satisfies the requirements for tax-deferral. There is a technical question as to whether shareholder-level tax-deferral in the split-off is available "by reason of" the reorganization, which creates uncertainty as to whether the applicable statutory exclusion would apply.
An overarching question is the extent to which covered corporations might change their behavior to avoid or reduce the Excise Tax. Such changes could include curbing buybacks, timing issuances to take place in the same year as buybacks, opting for dividends over buybacks and/or where possible, structuring M&A transactions to avoid causing technical repurchases as discussed above. The impact of the statute will depend in large part on regulatory guidance from Treasury.
1 According to estimates from the Joint Committee on Taxation, the Excise Tax is expected to raise more than $73 billion. See https://www.jct.gov/publications/2022/jcx-18-22/.
2 Finance Committee Chair Ron Wyden, D-Ore., August 6, 2022 remarks on the Senate floor; https://www.brown.senate.gov/newsroom/press/release/brown-wyden-tax-stock-buybacks.
3 An "established securities market" generally includes (i) a national securities exchange registered under section 6 of the Securities Exchange Act of 1934 ("Exchange Act"), such as the NYSE or NASDAQ, (ii) a national securities exchange that is exempt from the Exchange Act because of the limited volume of transactions, (iii) a foreign securities exchange that satisfies regulatory requirements that are analogous to the regulatory requirements under the Exchange Act (such as the London Stock Exchange or the Tokyo Stock Exchange), (iv) certain regional or local exchanges and (v) inter-dealer quotation systems that regularly disseminate firm buy or sell quotations by identified brokers or dealers by electronic means or otherwise (such as an OTC market).
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Why does a fruit tree's blooming already share much about the quality of its fruit-bearing?
Pollination plays a critical role in the formation of fruits.
This phase, even though it seems early, is the exact time that the future harvest is being sown.
After that, during the entire fruit formation phase, some good practices will help you produce high-quality fruits.
How can a fruit harvest be enhanced?
Several factors line up to influence a harvest, and each one can work towards making your orchard more productive.
It plays a major role. If you choose fruit tree varieties that are adapted to the climate of your area, you'll be guaranteeing it the best possible growing conditions.
For example, avoid planting peach trees in Maine or apple trees in arid Utah deserts.
Sometimes you must pair different varieties together to boost pollination.
Wind and insects are responsible for carrying pollen from one tree to the next: it is a crucial step of pollination, and thenceforth of fruit-bearing.
Certain varieties must be paired together, and pollen from any other variety simply won't provide adequate pollination.
Talk with a salesman in your local horticulture store or nursery to learn which pairings work best.
But there are some varieties, called self-pollinating varieties, that are able to fertilize themselves without any pollen from an outside tree.
Usually, these varieties are used when the size of the garden doesn't allow for planting more than one fruit tree.
For a tree to produce many fruits, your entire garden must be bursting with flowers.
It is the best way to attract insects that will pollinate your trees along with the other flowers.
Diversify flowering plants, perennials and annuals.
Choose nectar-rich blooms that attract honeybees due to the abundance of nectar, or generally any entomophilous species that attracts insects.
If you're planting a hedge around your fruit tree plantations, at all costs do consider setting up a mixed hedge.
Why does my fruit tree not bear fruit? Or so few?
It is often surprising to see your fruit tree with almost no fruits, knowing that the previous year's harvest was amazing!
But nature has its ways, and they are wise! A tree that has produced a huge quantity of fruits one year needs to rest the following year.
To reduce this phenomenon, you can prune the tree every year.
Remove vertical, climbing stems to promote the growth of horizontal, easy-to-pick branches.
This step will help you maximize fruit formation effectively.
Remove a portion of the fruits as soon as they form (thinning).


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Recent Release | 10 Jan 2023
The Global Green Economy: Understanding and capturing the opportunity
Economic Consulting Team
Oxford Economics
As each year passes, the climate emergency facing the planet becomes ever more alarming. But this trajectory is increasingly being met by the rapid emergence of new technologies and expertise that are focused on tackling it. As a result, we can now discern the emergence of a future green economy; one that harnesses human ingenuity to protect the planet's future.
But what is the green economy? How large is it? How will it grow? And how can it be developed in a way that drives prosperity and inclusiveness, as well as environmental sustainability?
These are the questions that a team of climate specialists, industry experts and economists from Arup and Oxford Economics spent the last 12 months addressing. Our goal is to help governments, investors and communities better understand the opportunities a green economy represents. In this study, we provide a new resource to support the strategic economic decision making required to seize those opportunities, and to place the global economy on an environmentally sustainable track. We estimate that the transition to a net zero emissions environment by 2050 will create new industries worth $10.3 trillion to the global economy by that same year.
The study addresses three key questions:
• What is the green economy, and what economic activities represent it?
• What is the size of the green economy? And what opportunities does the world's transition to a net zero emissions environment present?
• How can countries and companies identify and capture the right green economy opportunities?
Our economic consulting team are world leaders in quantitative economic analysis, working with clients around the globe and across sectors to build models, forecast markets and evaluate interventions using state-of-the art techniques. Lead consultants on this project were:
James Lambert
Director of Economic Consulting, Asia
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Direct +65 6850 0125
James is the Director of Oxford Economics' economic consulting services in Asia.
James moved to this role from Oxford Economics' London office, where he headed up a team dedicated to exploring the economic impact of technology. He delivered high profile studies on the growth of the digital economy, the impact of automation and the implications for the labour market.
Prior to joining Oxford Economics, James spent over six years in the Government Economics Service. He worked in economics teams of the Cabinet Office, the Foreign and Commonwealth Office and the Department for Transport. There, he gained experience in microeconomic analysis and impact assessment as well as international macroeconomics, economic risk analysis and energy security. In the FCO, James spent three years working on economic issues in East and South East Asia. He also previously worked for the International Labour Organization.
Lead Economist, Economics & Sustainability
Matt joined Oxford Economics' Economic Impact team in 2014. In his time with the company, he has worked on a diverse range of Economic Impact studies, including in the creative industries, tourism and retail sectors.
Between 2019 and 2022, Matt was based in our Singapore office, supporting the development of a specialist Economic Impact team there, before relocating back to London to work in the Economics and Sustainability team. Matt holds both a BSc (Hons) and an MSc (Hons) in Economics, from the University of Bristol.
Tom Rogers
Associate Director, Capital Projects and Assets Consulting
Private: Tom Rogers
Policymakers must be honest about the winners and losers of clean energy transition and building a green economy
Achieving a net zero and carbon neutral world by 2050 is the defining challenge of our age. It relies on many partners working together to shoulder great costs, and to do so as equitably and efficiently as possible. It is important for policymakers to be honest about the challenges businesses, investors, and consumers will have to face if we are to halt global warming on the sort of timescales scientists are telling us is necessary.
Competing on climate: Rewards are there for those who prioritise transition towards a green economy
Is a poor understanding of the advantages of going green the reason less than a third of companies have actually taken action to attain their sustainability goals? Competitive opportunities in industry disruption, new green markets and productivity gains from mitigation all await those with the necessary green ambitions and associated strategy to take advantage of the green opportunities.
$10.3 trillion: the value of the green economy opportunity
Greening the global economy – an Arup / Oxford Economics advisory perspective series The scientific consensus is clear: the impact of a failure to tackle climate change will be devastating. Higher concentrations of pollutants such as CO2 will push average temperatures up across the world, causing rising sea levels and extreme weather events that will…


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