Critical density in our expanding universe

[Positralino]

I am only a beginner in physics and have been reading popular books.
I read that the average mass-energy density of the universe determines its shape such as having uniform positive curvature, uniform negative curvature, or zero curvature if it equals the critical density. However, if spacetime is expanding, does that mean the mass-energy density of the universe is changing and the shape of the universe is changing? Moreover, if we speak of the universe having an infinite spatial extent and a finite amount of mass-energy, doesn't the mass-energy density of the universe be equal to zero?

 

[marcus]

... Moreover, if we speak of the universe having an infinite spatial extent and a finite amount of mass-energy,..

I don't know of anybody who speaks that way. In conventional mainstream cosmo, infinite spatial extent would entail infinite amount of mass-energy.

 

[marcus]

I read that the average mass-energy density of the universe determines its shape such as having uniform positive curvature, uniform negative curvature, or zero curvature if it equals the critical density. However, if spacetime is expanding, does that mean the mass-energy density of the universe is [declining] and the shape of the universe is changing? ...

That's a good question. However the critical density is also declining. So it's NOT necessarily true that simply because the average density is going down it has to eventually fall below critical.

I can think of two reasons it's a good question. One is the obvious one that if you think of the critical density as constant (rather than linked to other stuff making it fall off with time) then since the real density is declining you'd expect it might go below critical.

The main reason it's a good question though, I think, is that it leads into a lot of complicated issues to sort out. You could learn a lot by pursuing it. The first answers you will get won't necessarily be the best ones. there's interesting stuff below the surface that you just scratched. Welcome.

 

[marcus]

Not enough people seem to be using the google calculator to do cosmo calculations, so since you're new I'll invite you to try it. Maybe you will turn out to be someone who likes using it.

The neat thing is it knows a lot of units and constants, so you don't have to look them up.

Like for example the Hubble time is defined to be the reciprocal of H_o
It is a length of time 1/H_o that corresponds to the socalled Hubble radius (the distance which is growing exactly at the speed of light).

What value of H_o do you use? Lots of people use 71 km/s per Mpc.

The google search window doubles as a calculator. So copy this into the search window :
1/(71 km/s per Mpc)
And press space, or return...You should get 13.8 billion years.

the point is that it knows that Mpc means "megaparsec" and that this is a certain distance and it knows what the distance is in meters. It can do all the units conversion for you and give you the answer without your having to look stuff up in a book.

People should use it more. It also makes it easy for you to calculate the CRITICAL DENSITY, say as an energy density. If you like metric units like joule (energy) and cubic meter (volume), it can tell you the critical density in nanojoules per cubic meter.

And you will see how the critical density is NOT CONSTANT, but depends on the distance expansion rate H_o. Calculating the critical density is an easy exercise with the google calculator. It uses constants like c and G but the calculator knows them. If you want to try it, say.

 

[Chalnoth]

I read that the average mass-energy density of the universe determines its shape such as having uniform positive curvature, uniform negative curvature, or zero curvature if it equals the critical density.

The way I prefer to understand it is that it is about the balance between the rate of expansion and the energy density. This is mostly easily understood if we imagine a universe with only normal matter in it.

With just normal matter, we can imagine three possible situations:
1. The universe is expanding so rapidly compared to its density that the gravitational pull of the different bits of matter just aren't ever strong enough to stop the expansion, so it continues on forever.
2. The universe is expanding slowly enough that the gravitational pull of the matter is able to stop the expansion, also causing the universe to collapse back inward on itself.
3. An inbetween situation where the universe is expanding just fast enough so that it asymptotically approaches zero expansion into future infinity. So it gets really really close to stopping, but never actually does.

These three situations are the situations with an open, closed, and flat universe, respectively. Each has to do with how the density compares to the expansion rate. Both the density and the expansion rate do change moving into the future, but the answer to the question, "Will this universe ever recollapse?" never does change.

If you add in other components of the universe, such as dark energy, the link between curvature and the question, "Will this universe ever recollapse?" breaks down, unfortunately. But the fact that it is a comparison between the current expansion rate and the current energy density of the universe doesn't change.