# [Cosmology] Scale Factor Values

by ajclarke
Tags: cosmology, factor, scale, values
 P: 34 Hello. I have been working through some questions and answers to do with cosmology. One of them asks you to consider a model where: $$\Omega_{MO}=3$$ $$\Omega_{\Lambda O}=0.01$$ $$\Omega_{RO}=0$$ and asks you to show mathematically that the model re-collapses. Following through the math, I get three values of a: -14.87,1.51 and 13.36. Clearly the first can be disregarded and unphysical since a cannot be negative, but I can't decide whats the significance between the second two which allows me to isolate the value corresponding to collapse. Cheers. Adam
 P: 1,262 What 'math' are you following through with?
 PF Patron P: 183 If a is normalized time, then it may have zero diameter 14.87 time units in the past, first collapse 1.51 in the future, and a "recollapse" later. Not sure if that's correct though.
Mentor
P: 8,262

## [Cosmology] Scale Factor Values

What is the definition of $\Omega_{s0}$ for some species $s$? What is $\Omega_{\rm total 0}$ in the universe you are studying?
 Sci Advisor P: 4,596 Make use of the second Friedmann equation to make sure that when $H(a)$ goes to zero, $dH/da$ is negative.
P: 34
 Quote by zhermes What 'math' are you following through with?
I used the equation for the Hubble Parameter as a function of redshift, then changed this over to be a function of scale factor instead.

 Quote by cristo What is the definition of $\Omega_{s0}$ for some species $s$? What is $\Omega_{\rm total 0}$ in the universe you are studying?
$$\Omega_{total 0} = 1$$

I don't understand the first bitof the question I'm sorry.

 Quote by Chalnoth Make use of the second Friedmann equation to make sure that when $H(a)$ goes to zero, $dH/da$ is negative.
I'm uncertain as to how that determines which of the two remaining parameters is the recollapsing universe?
 Mentor P: 5,888 Use the second derivative test from elementary calculus. $a\left(t\right)$ has a local maximum at $t = t_1$ if $da/dt \left(t_1 \right) = 0$ and $d^2 a/dt^2 \left(t_1 \right) < 0$. To find $d^2 a/dt^2$, differentiate the Friedmann equation.