Universe expansion is slowing down

[Chalnoth]

Correct. Just when you see the increase in the rate of expansion that increase was billions of years ago, not now. If you want to know how the rate of expansion changed (or will change) over time you have to reverse the timescale.

I think you're a bit confused between the rate of expansion $H$ and the acceleration of the scale factor, $a(t)$.

The rate of expansion $H$ has always been decreasing. However, lately it has been decreasing more slowly, slowly enough that it leads to an accelerating expansion. How is this possible? Well, the rate of expansion $H$ is defined as:

$$H(t) = {1 \over a(t)}{da(t) \over dt}$$

I think the easiest way to see why a slowly-decreasing $H(t)$ leads to an accelerating expansion is to consider a constant $H(t) = H_0$.

$$H_0 = {1 \over a(t)}{da(t) \over dt}$$
$${da(t) \over dt} = H_0 a(t)$$

So a constant rate of expansion $H(t)$ means that change in the scale factor is proportional to the scale factor: this is exponential growth! Specifically:

$$a(t) = a(t=0) e^{H_0 t}$$

So a constant rate of expansion means that objects within the universe are accelerating away from one another exponentially fast. This isn't the situation we're in yet, but it appears that our universe is approaching this situation.

 

[RUTA]

I trust that the guys who earned the Nobel prize for proving that the expansion rate of the universe is increasing were correct, and that the expansion rate is not decreasing as you are claiming.

"Various alternatives to an accelerating universe have also been proposed. Whether such alternatives are viable remains to be seen, but the Nobel Committee for Physics has perhaps acted somewhat prematurely by selecting a preferred interpretation of the supernova projects’ data. The effect, intentional or not, is to bully the skeptics into silence, self-censorship, or ridicule, whereas good science proceeds with a healthy dose of skepticism and with open minds." http://www.physicstoday.org/resource/1/phtoad/v65/i2/p10_s1?view=print&bypassSSO=1

We just published an alternative in Class. Quant. Grav. last month whereby the universe is a decelerating Einstein-deSitter model (no cosmological constant, no dark energy, no acceleration) http://arxiv.org/abs/1110.3973. Our model fits the supernova data as well as the accelerating LambdaCDM (Einstein-deSitter plus cosmological constant).

Don't get me wrong, LCDM has also fit WMAP and BAO data better than alternatives (we haven't even tried that yet). So, the safe bet is accelerating expansion per LCDM. But, I wouldn't go so far as to claim the accelerating expansion has been "measured." It is a model dependent "acceleration."

 

[Drakkith]

Interesting Ruta. I'll be sure to take a look at the paper as soon as I get a chance. Thanks for the link.

 

[Chalnoth]

We just published an alternative in Class. Quant. Grav. last month whereby the universe is a decelerating Einstein-deSitter model (no cosmological constant, no dark energy, no acceleration) http://arxiv.org/abs/1110.3973. Our model fits the supernova data as well as the accelerating LambdaCDM (Einstein-deSitter plus cosmological constant).

Don't get me wrong, LCDM has also fit WMAP and BAO data better than alternatives (we haven't even tried that yet). So, the safe bet is accelerating expansion per LCDM. But, I wouldn't go so far as to claim the accelerating expansion has been "measured." It is a model dependent "acceleration."

This is the fundamental problem. Supernova data are, today, the data that constrain the accelerating universe the least. The real tests are the WMAP and BAO data. Once you add those it's next to impossible to have anything but an accelerating universe.

 

[Radrook]

Myslius, the universe has been accelerating since approximately 7 billion years after the big bang. NOT since the big bang itself. In fact, it was decelerating until roughly the 7 billion year mark. At that time, the density of dark energy (the cosmological constant, so it probably doesn't ever lose density) overcame the density of matter/dark matter, which falls very fast.

Absolutely true!

The Expanding Universe: From Slowdown to Speed Up
Distant supernovae are revealing the crucial time when the expansion of the universe changed from decelerating to accelerating


Currently the density of dark energy is higher than that of matter, but in the distant past the density of matter should have been greater, so the expansion should have been slowing down then.
http://www.scientificamerican.com/article.cfm?id=expanding-universe-slows-then-speeds

 

[Chronos]

According to theorists, if the universe is absolutely flat, the matter density of the universe is, and always will be, equal to its critical density since the end of the inflationary epoch.

 

[Chalnoth]

According to theorists, if the universe is absolutely flat, the matter density of the universe is, and always will be, equal to its critical density since the end of the inflationary epoch.

While strictly true, I'm pretty sure this isn't the case, as it requires perfect fine-tuning of the initial conditions of our universe.