<p>The light we see now is <em>not</em> a direct indication of how the galaxy was moving at the time the light was emitted. In the cosmological frame, the galaxies aren't moving (on average, at least); rather, space between them is expanding. The rate at which it is expanding is the Hubble parameter.</p>

<p>If cosmic expansion is homogeneous and isotropic, then all distances on the cosmological scale should be affected in the same manner, proportionally, unless other forces are involved. Thus the distance between some galaxy and us is affected in the same proportion as the wavelength of the light:
$$\frac{D_\text{now}}{D_\text{then}} = \frac{\lambda_\text{now}}{\lambda_\text{then}}\text{.}$$
The light we see now is a direct indication of the <em>scale factor</em>, i.e. by what factor the distance has grown since the time of emission. We can also consider distance $D$ as a function of cosmological time $t$ and define a <em>recession velocity</em> as the rate at which it is changing:
$$v_\text{r} \equiv \frac{\mathrm{d}D}{\mathrm{d}t} = \underbrace{\left[{\dot{D}}/{D}\right]}_{H(t)}D\text{.}$$ 
Therefore, the recession velocity <em>now</em> is given by the Hubble parameter $H(t)$ <em>now</em>.</p>

CC BY-SA 3.0
2014-06-11T06:48:52.883Z
But as I mentioned in the question, can it not be (mis)interpreted as the expansion being faster 10 billion years ago and slower 5 billion years ago?
Yashbhatt
CC BY-SA 3.0
2014-06-11T07:09:46.630Z
@Yashbhatt: What you observe is the redshift, which is (related to) the ratio of *distances*, present vs past. You're talking about changing *recessional velocities*. A changing rate of expansion is possibly (hence $H(t)$, not a constant), but the conclusion in your question is logically disconnected from the premises.
Stan Liou
CC BY-SA 3.0
2014-06-11T07:39:02.630Z
I think I have misinterpreted something. In $v = Hd$, the $d$ is the present distance to the galaxy or the distance to the galaxy when the light was emitted?
Yashbhatt
CC BY-SA 3.0
2014-06-11T07:53:56.963Z
@Yashbhatt: It's the present distance to the galaxy. Above, $\dot{D}$ is the rate of change of the distance to the galaxy. Note the that the Hubble parameter has $D$ in the denominator. (Assuming the galaxy has no "peculiar velocity", i.e. zero velocity through space in the cosmological frame--only recession due to expansion.)
Stan Liou
CC BY-SA 3.0
2014-06-11T07:55:43.297Z
But how do we find the present distance to the galaxy, it may be well beyond the cosmic horizon.
Yashbhatt
CC BY-SA 3.0
2014-06-11T08:04:22.527Z
@Yashbhatt: Distance measurements in astronomy tend to very imprecise, but you can look up, e.g., [cosmic distance ladder](http://en.wikipedia.org/wiki/Cosmic_distance_ladder) on wikipedia.
Stan Liou
CC BY-SA 3.0
2014-06-11T08:38:09.910Z
Which of these methods in particular is used to measure the distance to galaxies beyond the cosmic horizon?
Yashbhatt
CC BY-SA 3.0
2014-06-11T09:06:38.000Z
@Yashbhatt: There are no observable galaxies beyond the cosmic horizon, so none.
Stan Liou
CC BY-SA 3.0
2014-06-11T12:48:46.523Z
But how do we find a galaxy's current state/position?
Yashbhatt
CC BY-SA 3.0
2014-06-11T13:55:27.917Z
@Yashbhatt: modeling. Make another question, please. It's both off-topic to this question and the comment section is inappropriate for it anyway.
Stan Liou
CC BY-SA 3.0
2014-06-11T01:43:03.277Z
2014-06-11T01:43:03.277Z
Stan Liou
<p>According to Hubble's Law, the farther a galaxy is, the farther it is moving away. But do we take into account the fact that we are actually looking in the past?</p>

<p>For example, there are two galaxies A and B at distance of 5 and 10 billion years respectively. Now, when we observe A we are looking at how it was moving 5 billion years ago. The same applies for B. So, now we conclude that 5 billion years ago space was expanding at a slower rate while it was expanding comparatively faster 10 billion years ago. What's wrong with this conclusion?</p>

<space><redshift><expansion>
Is the expansion accelerating or Decelerating?
Yashbhatt
# Is the expansion accelerating or Decelerating?

(Asked by: username_0 on 2014-06-10)

According to Hubble's Law, the farther a galaxy is, the farther it is moving away. But do we take into account the fact that we are actually looking in the past?

For example, there are two galaxies A and B at distance of 5 and 10 billion years respectively. Now, when we observe A we are looking at how it was moving 5 billion years ago. The same applies for B. So, now we conclude that 5 billion years ago space was expanding at a slower rate while it was expanding comparatively faster 10 billion years ago. What's wrong with this conclusion?

**Tags:** space, redshift, expansion

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## 1 answers

### Answer by username_1 on 2014-06-11. Score: 4

The light we see now is *not* a direct indication of how the galaxy was moving at the time the light was emitted. In the cosmological frame, the galaxies aren't moving (on average, at least); rather, space between them is expanding. The rate at which it is expanding is the Hubble parameter.

If cosmic expansion is homogeneous and isotropic, then all distances on the cosmological scale should be affected in the same manner, proportionally, unless other forces are involved. Thus the distance between some galaxy and us is affected in the same proportion as the wavelength of the light:
$$\frac{D\_\text{now}}{D\_\text{then}} = \frac{\lambda\_\text{now}}{\lambda\_\text{then}}\text{.}$$
The light we see now is a direct indication of the *scale factor*, i.e. by what factor the distance has grown since the time of emission. We can also consider distance $D$ as a function of cosmological time $t$ and define a *recession velocity* as the rate at which it is changing:
$$v\_\text{r} \equiv \frac{\mathrm{d}D}{\mathrm{d}t} = \underbrace{\left[{\dot{D}}/{D}\right]}\_{H(t)}D\text{.}$$
Therefore, the recession velocity *now* is given by the Hubble parameter $H(t)$ *now*.

> **Comments:**
> **username_0**: But as I mentioned in the question, can it not be (mis)interpreted as the expansion being faster 10 billion years ago and slower 5 billion years ago?  
> **username_1**: @Yashbhatt: What you observe is the redshift, which is (related to) the ratio of *distances*, present vs past. You're talking about changing *recessional velocities*. A changing rate of expansion is possibly (hence $H(t)$, not a constant), but the conclusion in your question is logically disconnected from the premises.  
> **username_0**: I think I have misinterpreted something. In $v = Hd$, the $d$ is the present distance to the galaxy or the distance to the galaxy when the light was emitted?  
> **username_1**: @Yashbhatt: It's the present distance to the galaxy. Above, $\dot{D}$ is the rate of change of the distance to the galaxy. Note the that the Hubble parameter has $D$ in the denominator. (Assuming the galaxy has no "peculiar velocity", i.e. zero velocity through space in the cosmological frame--only recession due to expansion.)  
> **username_0**: But how do we find the present distance to the galaxy, it may be well beyond the cosmic horizon.  
> **username_1**: @Yashbhatt: Distance measurements in astronomy tend to very imprecise, but you can look up, e.g., [cosmic distance ladder](http://en.wikipedia.org/wiki/Cosmic_distance_ladder) on wikipedia.  
> **username_0**: Which of these methods in particular is used to measure the distance to galaxies beyond the cosmic horizon?  
> **username_1**: @Yashbhatt: There are no observable galaxies beyond the cosmic horizon, so none.  
> **username_0**: But how do we find a galaxy's current state/position?  
> **username_1**: @Yashbhatt: modeling. Make another question, please. It's both off-topic to this question and the comment section is inappropriate for it anyway.  

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