# What acceleration of universe means?

1. Jan 27, 2012

### minio

Sorry for such basic question, but am not able to get what it actually means? I know Hubbles "constant" is some 71 (km/s)/Mpc. Does acceleration of expansion means that the constant is getting larger? Or is it something completely different?

2. Jan 27, 2012

### minio

Sorry I meant "What acceleration of universe expansion means?".

3. Jan 27, 2012

### Fuzzy Logic

The hubble constant (H0) only reflects one moment in time, back when it was first observed.

If you extrapolate the hubble parameter (H) over time (H1, H2, etc, to HNOW), then it's not constant, it is accelerating.

4. Jan 27, 2012

### shifty88

It means its getting faster.

Isn't it vacuum energy, the mysterious dark energy. The energy of nothing that is responsible for the acceleration in the expansion rate of the universe

5. Jan 27, 2012

### minio

So "acceleration in universe expansion" simply means that Hubble constant is getting larger as time goes on? (from 70 to 80 and so on)

6. Jan 27, 2012

### George Jones

Staff Emeritus
No. Even though the expansion of the universe is accelerating, the Hubble constant is decreasing. Sorry, I don't have time to explain.

7. Jan 27, 2012

### bapowell

No, this is incorrect. The Hubble parameter is defined in terms of the scale factor, a(t), as
$$H = \frac{\dot{a}}{a}$$
(The Hubble constant is the Hubble parameter evaluated at the present time).
The scale factor simply governs the growth of measuring rods affixed to the expanding space (imagine a grid painted on a rubber sheet; as the sheet expands, the grid grows: a(t) determines this change in length scale). Now, by accelerated expansion what we mean is that the scale factor, a(t), has a positive second derivative: $\ddot{a}>0$.

Relating back to the Hubble parameter, by taking its derivative one finds
$$\dot{H} = \frac{\ddot{a}}{a} - H^2$$
so the answer to your question about how the Hubble parameter behaves during accelerated expansion is: it depends. For example, the simplest case of accelerated expansion is that due to a cosmological constant (a constant energy density.) In this case, $a(t) \propto e^{Ht}$: the scale factor grows exponentially in time (you can verify easily that this gives a positive $\ddot{a}$). Using the above equation for $\dot{H}$, one finds that $\dot{H}=0$ -- that the Hubble parameter in fact doesn't change at all!

EDIT: To make contact with George's post (that I just saw now), one finds that H indeed decreases for all other cases except the one I just showed you (the case of a cosmological constant.)

8. Jan 27, 2012

### juanrga

The Hubble constant is not a constant. and this is the reason for which you do not find it in a table of physical constants (where you can find G, h, c...)

It must be named constant by legacy issues, when cosmologists believed that Universe was static.

9. Jan 27, 2012

### Nabeshin

Well, no. The hubble constant came into being precisely when we learned the universe was NOT static, so that makes no sense.

It's called a constant because it's precisely a slope parameter (i.e. constant) in the Hubble equation: $v= H_0 d$. So for observational purposes, in the close-by approximation, it really is a constant. That's where the terminology comes from, but of course we know from the precise definition that at different epochs of the universe, an observer would measure different values for it.

10. Jan 27, 2012

### minio

bapowell:
So if I understand it correctly - Universe expansion is basically a speed at which is distance between two points increasing and Hubble parameter is about how fast are points passing certain point at fixed distance. So the speed of expansion is increasing, however it does not mean that $\ddot{a}$ is increasing just that $\ddot{a}$ > 0, but the value of $\ddot{a}$ could be decreasing over time. Am I right?

11. Jan 28, 2012

### juanrga

I was writing about the history of this topic not about some rewrite of it.

In 1929, Hubble discovered the empirical relation between redshift and distance: $cz= H_0 d$.

Hubble used the term "apparent velocities" to refer to cz and in 1931 wrote a letter to the Dutch cosmologist Willem de Sitter expressing his opinion on the theoretical interpretation of the redshift-distance relation:

Big bang cosmologists interpreted cz as a results of expanding velocity. Posteriorly, Hubble, not totally satisfied with Big Bang model, studied alternative models and published the Hubble & Tolman's paper in 1935:

In this static universe H was constant. Hubble also wrote:

Hubble original constant in his empirical law is reused in the modern big bang model as $V= H_0 d$, but here H is not a constant (some modern references are starting to use the more correct term "Hubble parameter").

Last edited: Jan 28, 2012
12. Jan 28, 2012

### George Jones

Staff Emeritus
The Hubble constant is not constant in time, but it is constant in space. In any FLRW universe, $H$ is constant and the expression $v = Hd$ is exact on any spatial hypersurface that results from considering an instant in cosmological time. On different spatial hypersurfaces (i.e., at different instants of cosmological time), $H$ has different values.

13. Jan 28, 2012

### juanrga

Right, but the original poster meaning of "constant" was clearly "constant in time". The quote that you are giving is my response to it, in that context, explaining that is not constant in time.

Moreover, I also give the argument of universal constants, which you are not considered. True constants as G, h, c... are constant in both space and time. The Hubble H is not and is not added to tables of physical constants.

14. Jan 28, 2012

### minio

No it was not. It was about what means "accelerated expansion of universe" and if it has something to do with Hubble constant. I know that Hubble constant is not constant in time, hence the quotes in original post.

My question was basically answered by bapowell. Now I am just curious if the acceleration means that $\ddot{a}$ is growing over time or that only $\ddot{a}$>0 and the actual size $\ddot{a}$ could change (both ways) over time.

15. Jan 28, 2012

### George Jones

Staff Emeritus
$\ddot{a}$ always increases. In the past, $\ddot{a}$ was negative, and has increased to its present positive value. $\ddot{a}$ grows exponentially for large $t$. A good analytical model is $a \left( t \right) = \sinh^{2/3} t$. See the spatially flat, matter-only Lemaitre model given on page 406 and in problem 15.23 in the book General Relativity: An Introduction for Physicists by Hobson, Efstathiou, and Lasenby, and see

http://arxiv.org/abs/0801.0552

equation (0.5).

16. Jan 28, 2012

### minio

Thak you. I think I get it now. Though I have to admit that I do not like it. Sadly observations seems to be against me...

17. Jan 28, 2012

### juanrga

My writing was sloppy. Sorry but I do not said that you did not knew. From what you wrote, it was evident that you knew that H varies with time. That was not my point.

As you correctly notice now you wrote "constant" between quotes. The fact you quoted "constant" implies that you were believing that others would interpret constant in the sense of constant in time; and you quoted the word for avoiding confusion. If you were believing that everyone else would interpret constant in the sense of constant in space you would not need quotes and merely would write

My original post was an attempt to avoid further confusion from others.

This kind of confusion about the term "constant", where some people can use it as meaning "constant in space", whereas others can use it as meaning "constant in time" is the reason for which Hubble parameter is a better name.

If you were written

you would not need to use quotes around words...

Last edited: Jan 28, 2012
18. Feb 2, 2012

### amarante

Hi,

how do we know that the Universe is accelerating? I know a bit about the Hubble Key Project. But I can not find the information how they concluded that the Universe has an accelerated expansion. Did they check their values with previous observations?

Thanks

19. Feb 2, 2012

### bapowell

The accelerated expansion of the universe is inferred from the relationship between luminosity distance and redshift. This relationship was determined to sufficiently high redshift by two teams in 1998 using type Ia supernovae as standard candles: the High-Z Supernova Search Team and the Supernova Cosmology Project. Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess were awarded the 2011 Nobel Prize in physics for this work.