Different FRW Cosmological Models

[QuarkDecay]

TL;DR

A chart of 10 different Cosmological Models is given. It contains information about the density, the curvature and their cosmological constant.
Need to put 1 or 2 "x" in the last 4 columns. One for t→0 and one for t→∞

ρο/a4	ρο/a3	k	Λ	Βig Bang	Big Crunch	Polynomial Expansion	Exponential Expansion
x		0
	x	0	>0
x		+1
	x	+1
	x	0	<0
x		-1
x		-1	>0
	x	0
	x	+1	>0
x		0	<0

 

[PeterDonis]

Are you asking for help in filling in the blanks?

 

[kimbyd]

Is this a homework question?

 

[QuarkDecay]

No it's not homework question. Don't remove it from this category please, because I think that's the best category for this. It's what I read in my book but I couldn't find where the answers are supposed to be.

The left part of the columns describes the characteristics of the Universe Model, and depending on these, it's supposed to be filled with 1 or 2 "x" on the right part.
For example, the Universe of the first row has a ρ_ο/a⁴ with flat curvature (k=0). ρ_ο/a³ and Λ are not filled in because they don't exist for this specific model.

I know that for the ρ_ο/a⁴ (which is the ρ_r) was bigger during the Big Bang phase. So I suppose that there must be an "x" on the Big Bang column. But I'm not sure about the k=0 after that, and what are the two expansions supposed to mean? Expotential expansion= inflation? Polynomial expansion = the "normal" expansion rate we currently have?

 

[PeterDonis]

the Universe of the first row has a ρο/a4

What does "has a $\rho_0 / a^4$" mean?

 

[kimbyd]

What does "has a $\rho_0 / a^4$" mean?

I'm sure it's talking about a radiation-dominated universe, where the density scales as $1/a^4$.

The left part of the columns describes the characteristics of the Universe Model, and depending on these, it's supposed to be filled with 1 or 2 "x" on the right part.
For example, the Universe of the first row has a ρ_ο/a⁴ with flat curvature (k=0). ρ_ο/a³ and Λ are not filled in because they don't exist for this specific model.

I know that for the ρ_ο/a⁴ (which is the ρ_r) was bigger during the Big Bang phase. So I suppose that there must be an "x" on the Big Bang column. But I'm not sure about the k=0 after that, and what are the two expansions supposed to mean? Expotential expansion= inflation? Polynomial expansion = the "normal" expansion rate we currently have?

It's asking what the eventual fate of the universe in question is. Will it expand forever, or will it recollapse? If it expands forever, what will the function $a(t)$ look like? Will it be a polynomial like $a(t) = t^b$, or will it be exponential like $a(t) = e^{bt}$ (where $b$ is some constant in either case)?

And no, exponential expansion does not mean inflation. Inflation has near-exponential expansion, yes, but it's not the only way to get exponential expansion.

BTW, you might want to check the LaTeX guide link near the bottom of this page.

Edit: Also, $k$ and $\Lambda$ always exist. It's probably not saying they don't exist, but rather that their values are zero in those cases.

 

[kimbyd]

Oh! And some of the answers are "it's ambiguous", meaning it depends upon the specific numbers.

 

[PeterDonis]

I'm sure it's talking about a radiation-dominated universe

Yes, you know that, and I know that, but I want to see if the OP knows that.