# Universe acceleration

1. Jul 1, 2009

### Ranku

When did the accelerating expansion of the universe start?

2. Jul 1, 2009

3. Jul 1, 2009

### Ranku

In other places the number quoted is 5 Gyrs or 4.5 Gyrs ago. Here it is 7 Gyrs. I'm confused by such discrepancies! Could somebody give me a clean consensus number quoting professional publications, like we have for the age of the universe?

4. Jul 1, 2009

### marcus

Anything anybody finds in the literature is likely to be old, before the new Riess numbers came out.

I don't know anything more authoritative than assuming near spatial flatness and the standard LCDM model, where the Friedman acceleration equation governs what you asked about.

You can solve that yourself and get that the redshift at changeover had to be around z = 0.82 or z = 0.83. That means that changeover happened at roughly half the current expansion age.

Like 6.7 billion years. The current age being 13.4 billion years (with the new Riess numbers).

I would shy away from trying to be too definite because a lot of things about the standard model are still being checked and verified. Are we really really sure that the dark energy density doesn't change over time? No. It just seems to be constant and assuming that gives a pretty good fit to the data, but it is still being checked.

===========================

Ranku, in case you want to solve the Friedman equation and get the answer here by yourself. Google "Friedman equations" and go to Wiki and you will see two equations, one of them tells you what a''/a is.
a is the scale factor, and acceleration simply means a'' > 0
So you merely have to solve for a'' = 0

And the equation basically is that this ratio (which you want to be zero) is equal to some constant times (-rhomatter + 2rhoLambda)
So the thing in parenthesis must be zero at changeover. And that means that twice the dark energy density must equal the (energy) density of matter.

By the new Riess numbers we can say that the current matter density (including dark matter) is 0.23 nanojoules per cubic meter.
And we can say that the dark energy density (which we assume constant) is 0.70 nanojoules per cubic meter, so twice that is 1.4 nanojoules per cubic meter.

To find the changeover we go back in time until the the matter density equals 1.4 nanojoules per cubic meter.
Now 1+z is the distance expansion factor between here and redshift z. So (1+z)3 is the volume expansion factor. So if you go back in time to redshift z, then the matter density is (1+z)3 * 0.23 nanojoules per cubic meter.

So you just have to solve (1+z)3 * 0.23 = 1.4

(1+z)3 = 1.4/0.23

that will tell you z and then the calculator will tell you age etc if wanted.

Last edited: Jul 1, 2009
5. Jul 2, 2009

Thanks.

6. Jul 2, 2009

### Chalnoth

Well, the problem here for me is that in cosmology, we rarely bother to consider these sorts of questions. They aren't very useful for understanding what causes the expansion, or the way in which the universe behaves. As a result, it would take a significant amount of work to transition from the parameters that are estimated to the uncertainties in questions such as this one. It wouldn't surprise me at all if, at the current time, the uncertainty on when the universe started accelerating was actually that large.