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Cosmology problem

  1. Mar 8, 2013 #1
    1. The problem statement, all variables and given/known data
    i i am trying to derive [itex] \dot{\rho_{R}}+4H\rho_{R}-\Gamma_{\phi}\rho_{\phi}=0[/itex] as in Kolb an turner (Boltzmann describing reheating).

    Is the correct approach to, use the 1st law dU=dQ-pdV, but what would dQ be?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 10, 2013 #2
    That is just the equation of conservation of energy, with an extra term with transfers energy from the inflaton to radiation.
     
  4. Mar 10, 2013 #3
    how though can it be derived?
    I no that: [itex] dU=(a^{3}\rho_{R})[/itex] and [itex]1/3\rho dV= pdV[/itex], but Im not sure about dQ.

    It is obviously then [itex]\rho_R d(a^3)+a^{3}d\rho_{R}=dQ - 1/3\rho_{R}d(a^3)[/itex] Then by dividing through by dt one can get [itex]\dot{\rho}_{R}+4H\rho_{R} -\frac{dQ}{dt} =0 [/itex].

    I don't see how one can justify [itex] \Gamma_{\phi}\rho_{\phi}=\frac{dQ}{dt} [/itex]
     
  5. Mar 10, 2013 #4
    I don't see how you can justify using the first law in that form, when clearly in reheating the number of particles is not conserved. It's my understanding that the [itex]\Gamma \rho[/itex]-term is just phenomenological.
     
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