Hubble's law and expansion question

In summary, the conversation is about ranking the ages of three universes (A, B, and C) based on their critical density, acceleration, and emptiness. The solution involves solving the Friedman and fluid equations and using the Hubble constant to calculate the age of each universe. It is suggested that Universe C is the oldest, followed by Universe A, and then Universe B. However, the accuracy of this solution may depend on the given information and the course level.
  • #1
tortin
2
0
Hi, I was looking through past exams for one of my courses, and I came across a question I wasn't quite sure how to do, so I was wondering if anyone could give some hints (or possibly the rationale for solution), thanks!

Homework Statement



Observers in three universes A, B, and C measure identical constants. However, universe A is a critical universe (i.e. p = pc (with c being critical density), Universe B is an accelerating universe, and Universe C is close to being an empty universe (i.e. p<<pc or p~0). Rank the ages of the three universes as measured by these observers from largest to smallest, and explain your reasoning.

Homework Equations


None really...

The Attempt at a Solution


I'm not quite sure what you can infer about the age of A if it's a critical universe, because it always stays flat with p = pc. C is probably the oldest universe, since it's emptying out, and I'd guess B is younger than C, since it's accelerating so not yet emptied out.

However, I was also wondering what the relevance of the identical Hubble constants would give in this problem.Thanks for anyone who can give some help / hints!

edit - maybe this should be in advanced physics forum?
 
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  • #2
I think you're going to have to solve the Friedman and fluid equations for each case and compare the estimation of the ages you get in terms of the Hubble constant.
 
  • #3
As Kurdt said, you should start with your basic Friedmann equation and solve to find the dependence of scale factor [tex]\dot{R}[/tex] with time, t.

Hints:

Since the scale factor directly relates to the Hubble constant you can work out the age for each universe using:

[tex]H(t)[/tex] = [tex]\frac{\dot{R}}R[/tex]

For the universe of critical density we then use our critical density relation:

[tex]\rho_c = \frac{3 H^2}{8 \pi G}[/tex]

which applies for a k=0, or a flat, universe.

For an accelerating universe [tex]\Lambda[/tex], the cosmological constant, is now non zero.

Edit: Shouldn't this be in advanced physics?
 
  • #4
astrorob said:
As Kurdt said, you should start with your basic Friedmann equation and solve to find the dependence of scale factor [tex]\dot{R}[/tex] with time, t.

Hints:

Since the scale factor directly relates to the Hubble constant you can work out the age for each universe using:

[tex]H(t)[/tex] = [tex]\frac{\dot{R}}R[/tex]

For the universe of critical density we then use our critical density relation:

[tex]\rho_c = \frac{3 H^2}{8 \pi G}[/tex]

which applies for a k=0, or a flat, universe.

For an accelerating universe [tex]\Lambda[/tex], the cosmological constant, is now non zero.

Edit: Shouldn't this be in advanced physics?

Hmm, so for Universe A (the critical one), we would have:
(removing the constants 8piG/3)

[tex]\Omega \propto \frac{\rho}{H(t)^{2}}[/tex]
However, [tex]H(t) = \frac{\dot{R}}R[/tex], so we can replace it such that:
[tex]\dot{R}^{2}\Omega \propto \rho[/tex]
[tex]\rho \propto \Omega z^{2}[/tex] (z being redshift)
So for universe A, [tex]\Omega[/tex] is 1, z would be larger than universe B, since [tex]\Omega[/tex] is close to 0, so A is older than B.

for universe C, addition of a cosmological constant would make z larger than A, giving the age as: C>A>B (in order of age)

would that be correct? (but it's assuming different Hubble parameters for each universe..)

I'm trying to do this more intuitively, since it's a first year course (and the Freidmann equation wasn't given on the exam), and although we did cover the equation, it seems a bit unlikely we'd have to calculate anything...

thanks!
 
  • #5
It depends of course on the class you're doing. I'd check the notes very carefully, but I'd be surprised if for a first year course they hadn't given you some sort of graph depicting the density parameter at various values. You should be able to work out the answer from this. I was perhaps being a bit too zealous when I suggested my original post.
 

What is Hubble's Law?

Hubble's Law states that the farther away a galaxy is from us, the faster it is moving away from us.

How does Hubble's Law relate to the expansion of the universe?

Hubble's Law is evidence for the expansion of the universe, as it shows that all galaxies are moving away from each other.

What is the significance of the constant in Hubble's Law?

The constant in Hubble's Law, known as the Hubble constant, is used to calculate the rate of expansion of the universe and provides important information about the age and size of the universe.

Has Hubble's Law been proven?

Hubble's Law has been extensively tested and confirmed through multiple observations and experiments, making it one of the most well-supported theories in astrophysics.

What are the implications of Hubble's Law for the future of the universe?

Hubble's Law suggests that the universe will continue to expand indefinitely, with galaxies becoming increasingly distant from each other. This could ultimately lead to the "heat death" of the universe, where all matter and energy is evenly distributed and everything is at a uniform and low temperature.

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