Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

[Cosmology] Scale Factor Values

  1. May 12, 2011 #1
    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 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
     
  2. jcsd
  3. May 12, 2011 #2
    What 'math' are you following through with?
     
  4. May 12, 2011 #3

    BillSaltLake

    User Avatar
    Gold Member

    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.
     
  5. May 12, 2011 #4

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    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?
     
  6. May 13, 2011 #5

    Chalnoth

    User Avatar
    Science Advisor

    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.
     
  7. May 13, 2011 #6
    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.

    [tex]\Omega_{total 0} = 1[/tex]

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

    I'm uncertain as to how that determines which of the two remaining parameters is the recollapsing universe?
     
  8. May 13, 2011 #7

    Chalnoth

    User Avatar
    Science Advisor

    If the derivative of the Hubble parameter is negative, then it's recollapsing.
     
  9. May 13, 2011 #8

    BillSaltLake

    User Avatar
    Gold Member

    Don't you have Ωtotal0 equal to 3.01, instead of unity?
     
  10. May 13, 2011 #9

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: [Cosmology] Scale Factor Values
  1. Scaling cosmologies (Replies: 4)

  2. Scale factor (Replies: 14)

Loading...