Introduction to Cosmology Ryden · Problem 10.3

Inflation and the Very Early Universe

Physics — Astrophysics · inflation-false-vacuum-reheating

Problem

It has been speculated that the present-day acceleration of the universe is due to the existence of a false vacuum, which will eventually decay. Suppose that the energy density of the false vacuum is εΛ=0.69εc,0=3360 MeV m−3\varepsilon_\Lambda = 0.69\varepsilon_{c,0} = 3360\ \rm{MeV\,m^{-3}}, and that the current energy density of matter is εm,0=0.31εc,0=1510 MeV m−3\varepsilon_{m,0} = 0.31\varepsilon_{c,0} = 1510\ \rm{MeV\,m^{-3}}. What will be the value of the Hubble parameter once the false vacuum becomes strongly dominant? Suppose that the false vacuum is fated to decay instantaneously to radiation at a time tf=50t0t_f = 50t_0. (Assume, for simplicity, that the radiation takes the form of blackbody photons.) To what temperature will the universe be reheated at t=tft = t_f? What will the energy density of matter be at t=tft = t_f? At what time will the universe again be dominated by matter?

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