What acceleration of universe means?

[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?

 

[minio]

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

 

[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 H_NOW), then it's not constant, it is accelerating.

 

[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

 

[minio]

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

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

 

[George Jones]

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

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

 

[bapowell]

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

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.)

 

[juanrga]

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?

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.

 

[Nabeshin]

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.

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.

 

[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?

 

[juanrga]

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.

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:

We use the term "apparent velocities" in order to emphasize the empirical feature of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority.

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:

both incline to the opinion, however, that if the red-shift is not due to recessional motion, its explanation will probably involve some quite new physical principles [... and] use of a static Einstein model of the universe, combined with the assumption that the photons emitted by a nebula lose energy on their journey to the observer by some unknown effect, which is linear with distance, and which leads to a decrease in frequency, without appreciable transverse deflection.

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

The observations may be fitter into either of two different types of universe... If red-shifts are not velocity sifts, the apparent distribution agrees with that in an Einstein static model of the universe or an expanding homogeneous model with an inappreciable rate of expansion... If red-shifts are velocity shifts which measure the rate of expansion, the expanding models are definitively inconsistent with the observations unless a large positive curvature ... is postulated... The high density suggest that the expanding models are a forced interpretation of the observational results.

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").

 

[George Jones]

The Hubble constant is not a constant.

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.

 

[juanrga]

The Hubble constant is not constant in time, but it is constant in space.

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.

 

[minio]

Right, but the original poster meaning of "constant" was clearly "constant in time".

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.

 

[George Jones]

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.

$\ddot{a}$ 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).

 

[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...

 

[juanrga]

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 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.

Your original post included:

I know Hubbles "constant" is some 71 (km/s)/Mpc.

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

I know Hubbles constant is some 71 (km/s)/Mpc.

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

I know Hubbles parameter is some 71 (km/s)/Mpc.

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

 

[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

 

[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.