<p>The recessional velocity $v$ of an object depends on two things: firstly it depends on how faraway an object is in terms of proper distance $D$, and secondly on the rate of the Universe's expansion as a function of cosmological time $t$, which is best expressed as the Hubble parameter $H(t)$. Specifically:</p>

<p>$$v = D \times H(t)$$</p>

<p>It's worth noting that this equation is slightly vacuous as it is merely the definition of recessional velocity, which is not something that can be directly measured.</p>

<p>As recessional velocity depends not just on a function of $t$, but also on $D$, the question as to whether objects are receding from us faster than ever before could be answered in several ways. Before I look at the different ways we could answer your question, I will note a few things. Firstly the definition of the Hubble parameter is:</p>

<p>$$H^2(t) = \bigg( \frac{\dot{a}(t)}{a(t)}\bigg)^2$$</p>

<p>where $a(t)$ is the scale factor which describes how the scale of the Universe changes with $t$, and $\dot{a}(t)$ is the first derivative of the scale factor with respect to $t$. Due to cosmological observations, the Universe is said to contain dark energy which causes the Universe's expansion to accelerate. What is meant by this is that at the current time $\ddot{a}(t) &gt; 0$ where $\ddot{a}(t)$ is the second derivative of the scale factor with respect to time.</p>

<p>The first way we could look at your question is we could ask whether galaxies currently at a distance $D_0$ are receding faster than other galaxies that were previously at distance $D_0$.  </p>

<p>From the definition of accelerating expansion and the Hubble parameter we can see that accelerating expansion does <strong>not</strong> imply that the answer to this question is "yes" and in fact if we assume dark energy takes the form of a cosmological constant (ignoring cosmic inflation), and we delve into the dynamics of the Universe, we find that galaxies currently at $D_0$ must be receding from us slower than the galaxies that were previously at $D_0$ were receding when they were at $D_0$. So in this particular sense the Universe's expansion is slowing down, even though we usually describe it as accelerated.</p>

<p>The second way we could answer your question is to ask whether the recessional velocity of any given galaxy is larger now than it has ever been in the past.  </p>

<p>The answer to this question is more difficult as accelerated expansion does imply that the recessional velocity of a given galaxy increase with time, but the Universe's rate of expansion in previous epochs was decelerating. However, again taking dark energy as taking the form of a cosmological constant, we see that the answer is that galaxies achieve their highest recessional velocities twice: firstly at the Big Bang, and secondly in the infinite future. So the answer to this question is that galaxies are <strong>not</strong> currently receding from us faster than they have been at all previous times.</p>

<p>Recession velocity is different from peculiar velocity (i.e. the local velocity with respect to the CMB). We could add the two to find the 'real velocity', but as I've noted recession velocity doesn't have a direct physical meaning so what this 'real velocity' actually means is not straightforward. </p>

<p>Expansion is homogeneous, whereas the vacuum around a black hole is not homogeneous, so in this sense the 'sucking' of a black hole is not the opposite of expansion.</p>

CC BY-SA 3.0
2015-07-11T15:51:56.483Z
I just don't understand what the scale factor is. I know it is a function of time, but what function exactly? Like for example, f(x)=sin x is a function. So what function represents a(t)?
set5
CC BY-SA 3.0
2015-03-14T20:52:57.497Z
2016-10-07T18:00:07.283Z
2016-10-07T18:00:07.283Z
John Davis
<p>Are all galaxies moving away from us at constant speed even those that may be moving in our direction as the space is being formed? How does nothingness appear to push matter? A black hole sucks as space is compressing (being stretched without stopping) or compressed (like how our Sun pulling all planets) and is it the opposite phenomenon that show universe is expanding?</p>

CC BY-SA 3.0
2015-03-14T15:28:37.497Z
Please elaborate since I am not certain what you are asking.
LDC3
CC BY-SA 3.0
2015-03-14T22:57:18.353Z
http://astronomy.stackexchange.com/questions/305/space-expansion-in-layman-terms?lq=1
Mithoron
CC BY-SA 3.0
2015-03-14T23:04:19.347Z
May I clarify my questions:
user6760
CC BY-SA 3.0
2015-03-14T23:42:28.800Z
Q1: We observed that the rate of expansion of space is increasing, what does this effect had on the gravitational pull between Andomeda Galaxy and us as will as with all other galaxies? I'm confused how dark energy came into the picture and it only interact with space exclusively, how do we know if dark energy is indeed affecting space directly or simply interact with anything that had mass?
user6760
CC BY-SA 3.0
2015-03-15T00:04:33.307Z
Q2: Relativity explained that massive object bends space around it inducing an effect as gravity, is there any way to observed what is happening to the space within the event horizon? Maybe inside the event horizon space is collapsing at increasing rate over time just as the opposite phenomenon showing our current rate of expansion of space?
user6760
CC BY-SA 3.0
2015-03-15T00:05:49.423Z
I don't think Q1 relates very well to your orginal question. See this very recent question for a discussion http://astronomy.stackexchange.com/questions/10121/expansion-of-space for how expansion acts on a smaller scale. We know even less about how dark energy is distributed on a small scale.
John Davis
CC BY-SA 3.0
2015-03-15T00:15:37.880Z
I agree Q1 is strayed from my original and I'm still studying the answers pls excuse me english is my second language sorry.
user6760
CC BY-SA 3.0
2015-03-15T00:31:23.667Z
I delved a little into Q2 at the foot of my answer. To go a little further you could probably create a tortuous anti-analogy between the vacuum around a black hole and cosmological expansion, but really cosmological collapse (as seen in some cosmological models) is the opposite of cosmological expansion.
John Davis
<galaxy><universe><cosmology><expansion>
Are galaxies moving away from us faster than before?
user6760
# Are galaxies moving away from us faster than before?

(Asked by: username_0 on 2015-03-14)

Are all galaxies moving away from us at constant speed even those that may be moving in our direction as the space is being formed? How does nothingness appear to push matter? A black hole sucks as space is compressing (being stretched without stopping) or compressed (like how our Sun pulling all planets) and is it the opposite phenomenon that show universe is expanding?

**Tags:** galaxy, universe, cosmology, expansion

> **Comments:**
> **username_1**: Please elaborate since I am not certain what you are asking.  
> **username_2**: http://astronomy.stackexchange.com/questions/305/space-expansion-in-layman-terms?lq=1  
> **username_0**: May I clarify my questions:  
> **username_0**: Q1: We observed that the rate of expansion of space is increasing, what does this effect had on the gravitational pull between Andomeda Galaxy and us as will as with all other galaxies? I'm confused how dark energy came into the picture and it only interact with space exclusively, how do we know if dark energy is indeed affecting space directly or simply interact with anything that had mass?  
> **username_0**: Q2: Relativity explained that massive object bends space around it inducing an effect as gravity, is there any way to observed what is happening to the space within the event horizon? Maybe inside the event horizon space is collapsing at increasing rate over time just as the opposite phenomenon showing our current rate of expansion of space?  
> **username_3**: I don't think Q1 relates very well to your orginal question. See this very recent question for a discussion http://astronomy.stackexchange.com/questions/10121/expansion-of-space for how expansion acts on a smaller scale. We know even less about how dark energy is distributed on a small scale.  
> **username_0**: I agree Q1 is strayed from my original and I'm still studying the answers pls excuse me english is my second language sorry.  
> **username_3**: I delved a little into Q2 at the foot of my answer. To go a little further you could probably create a tortuous anti-analogy between the vacuum around a black hole and cosmological expansion, but really cosmological collapse (as seen in some cosmological models) is the opposite of cosmological expansion.  

---

## 1 answers

### Answer by username_3 on 2015-03-14. Score: 2 | Accepted answer

The recessional velocity $v$ of an object depends on two things: firstly it depends on how faraway an object is in terms of proper distance $D$, and secondly on the rate of the Universe's expansion as a function of cosmological time $t$, which is best expressed as the Hubble parameter $H(t)$. Specifically:

$$v = D \times H(t)$$

It's worth noting that this equation is slightly vacuous as it is merely the definition of recessional velocity, which is not something that can be directly measured.

As recessional velocity depends not just on a function of $t$, but also on $D$, the question as to whether objects are receding from us faster than ever before could be answered in several ways. Before I look at the different ways we could answer your question, I will note a few things. Firstly the definition of the Hubble parameter is:

$$H^2(t) = \bigg( \frac{\dot{a}(t)}{a(t)}\bigg)^2$$

where $a(t)$ is the scale factor which describes how the scale of the Universe changes with $t$, and $\dot{a}(t)$ is the first derivative of the scale factor with respect to $t$. Due to cosmological observations, the Universe is said to contain dark energy which causes the Universe's expansion to accelerate. What is meant by this is that at the current time $\ddot{a}(t) > 0$ where $\ddot{a}(t)$ is the second derivative of the scale factor with respect to time.

The first way we could look at your question is we could ask whether galaxies currently at a distance $D\_0$ are receding faster than other galaxies that were previously at distance $D\_0$.

From the definition of accelerating expansion and the Hubble parameter we can see that accelerating expansion does **not** imply that the answer to this question is "yes" and in fact if we assume dark energy takes the form of a cosmological constant (ignoring cosmic inflation), and we delve into the dynamics of the Universe, we find that galaxies currently at $D\_0$ must be receding from us slower than the galaxies that were previously at $D\_0$ were receding when they were at $D\_0$. So in this particular sense the Universe's expansion is slowing down, even though we usually describe it as accelerated.

The second way we could answer your question is to ask whether the recessional velocity of any given galaxy is larger now than it has ever been in the past.

The answer to this question is more difficult as accelerated expansion does imply that the recessional velocity of a given galaxy increase with time, but the Universe's rate of expansion in previous epochs was decelerating. However, again taking dark energy as taking the form of a cosmological constant, we see that the answer is that galaxies achieve their highest recessional velocities twice: firstly at the Big Bang, and secondly in the infinite future. So the answer to this question is that galaxies are **not** currently receding from us faster than they have been at all previous times.

Recession velocity is different from peculiar velocity (i.e. the local velocity with respect to the CMB). We could add the two to find the 'real velocity', but as I've noted recession velocity doesn't have a direct physical meaning so what this 'real velocity' actually means is not straightforward.

Expansion is homogeneous, whereas the vacuum around a black hole is not homogeneous, so in this sense the 'sucking' of a black hole is not the opposite of expansion.

> **Comments:**
> **username_4**: I just don't understand what the scale factor is. I know it is a function of time, but what function exactly? Like for example, f(x)=sin x is a function. So what function represents a(t)?  

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