Age of Universe @ 1 MeV, 1 GeV & 1014 GeV: Calculation

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The discussion focuses on calculating the age of the universe at specific radiation temperatures of 1 MeV, 1 GeV, and 10^14 GeV within a Robertson-Walker universe framework. It highlights the importance of mass density and the effective number of relativistic spin states, g*, in determining energy density. The current mass density is defined using parameters such as Hubble's constant and the present radiation temperature of 2.725 K. The conversation shifts towards the necessity of providing attempts or methodologies to solve the calculations rather than just seeking answers. The thread emphasizes the educational aspect of understanding cosmological principles through practical application.
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Assume that we live in a Robertson-Walker universe with matter, radiation and curvature. The present mass density is ρm = 3Ω0H20/(8πG), where H0 = 100 h km s-1 Mpc-1 and Ω0(1+ρr,0/ρm;0) ≤ 1 (i.e., k ≤ 0). The present radiation temperature is T0 = 2.725 K.
Assume that only photons, with present temperature T0 = 2.725K contribute to the radiation; ignore neutrinos in this problem.
How old was the universe when the radiation temperature was 1 MeV? 1GeV?
1014 GeV? (Hint: you need g*, the effective number of relativistic spin states contributing to the energy density. At 1 GeV g* = 61.75 and at 1014 GeV, g* = 106.75 without supersymmetry or double this with SUSY.)
Thanks so much!
 
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This looks like a homework question, as such I am moving to the relevant homework forum. What attempts have you made the answer the question?
 
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