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[Cosmology] Scale Factor Values 
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#1
May1211, 02:13 PM

P: 35

Hello.
I have been working through some questions and answers to do with cosmology. One of them asks you to consider a model where: [tex]\Omega_{MO}=3 [/tex] [tex]\Omega_{\Lambda O}=0.01 [/tex] [tex]\Omega_{RO}=0 [/tex] and asks you to show mathematically that the model recollapses. 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 


#2
May1211, 04:35 PM

P: 1,261

What 'math' are you following through with?



#3
May1211, 04:49 PM

PF Gold
P: 184

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.



#4
May1211, 04:51 PM

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P: 8,317

[Cosmology] Scale Factor Values
What is the definition of [itex]\Omega_{s0}[/itex] for some species [itex]s[/itex]? What is [itex]\Omega_{\rm total 0}[/itex] in the universe you are studying?



#5
May1311, 12:36 AM

Sci Advisor
P: 4,805

Make use of the second Friedmann equation to make sure that when [itex]H(a)[/itex] goes to zero, [itex]dH/da[/itex] is negative.



#6
May1311, 05:29 AM

P: 35

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


#7
May1311, 06:10 AM

Sci Advisor
P: 4,805




#8
May1311, 11:34 AM

PF Gold
P: 184

Don't you have Ω_{total0} equal to 3.01, instead of unity?



#9
May1311, 01:09 PM

Mentor
P: 6,246

Use the second derivative test from elementary calculus. [itex]a\left(t\right)[/itex] has a local maximum at [itex]t = t_1[/itex] if [itex]da/dt \left(t_1 \right) = 0[/itex] and [itex]d^2 a/dt^2 \left(t_1 \right) < 0[/itex]. To find [itex]d^2 a/dt^2 [/itex], differentiate the Friedmann equation.



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