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Trifis

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It is not clear to me, why textbooks do not mention an upper bound for the e-foldings of the basic inflation theory.

To my knowledge, in order to deal with the flatness problem, we require:

[tex] \frac{Ω^{-1}(t_0)-1}{Ω^{-1}(t_i)-1} = \frac{Ω^{-1}(t_0)-1}{Ω^{-1}(t_e)-1} \frac{Ω^{-1}(t_e)-1}{Ω^{-1}(t_i)-1} = \left( \frac{a(t_i)}{a(t_e)} \right)^2 \left[ \left( \frac{T_{eq}}{T_0} \right) \left( \frac{T_e}{T_{eq}} \right)^2 \right] ≈ 1 [/tex]

where [itex] 0, i, e, eq [/itex] are the indices, which denote respectively the current time, the beginning of the inflation, the ending of the inflation (GUT scale) and the time of radiation/matter equality. The values [itex] T_0 ≈ 10^{-13}GeV, T_{eq} ≈ 10^{-9}GeV [/itex] are more or less "certain" and the value for [itex] T_e [/itex] is constrained and considered to be at the GUT scale ([itex] ~ 10^{15}GeV [/itex]). As a result, we get a constraint for [itex] \frac{a(t_i)}{a(t_e)} [/itex] and using the above values, we get: [itex] \frac{a(t_i)}{a(t_e)} ≈ 10^{-52} [/itex], which corresponds to the classical 60 e-foldings.

Prof. Susskind states here:

that 1000 e-foldings could work equally well. I cannot understand, why this is the case, since [itex] T_e [/itex] cannot get any arbitrary values.

To my knowledge, in order to deal with the flatness problem, we require:

[tex] \frac{Ω^{-1}(t_0)-1}{Ω^{-1}(t_i)-1} = \frac{Ω^{-1}(t_0)-1}{Ω^{-1}(t_e)-1} \frac{Ω^{-1}(t_e)-1}{Ω^{-1}(t_i)-1} = \left( \frac{a(t_i)}{a(t_e)} \right)^2 \left[ \left( \frac{T_{eq}}{T_0} \right) \left( \frac{T_e}{T_{eq}} \right)^2 \right] ≈ 1 [/tex]

where [itex] 0, i, e, eq [/itex] are the indices, which denote respectively the current time, the beginning of the inflation, the ending of the inflation (GUT scale) and the time of radiation/matter equality. The values [itex] T_0 ≈ 10^{-13}GeV, T_{eq} ≈ 10^{-9}GeV [/itex] are more or less "certain" and the value for [itex] T_e [/itex] is constrained and considered to be at the GUT scale ([itex] ~ 10^{15}GeV [/itex]). As a result, we get a constraint for [itex] \frac{a(t_i)}{a(t_e)} [/itex] and using the above values, we get: [itex] \frac{a(t_i)}{a(t_e)} ≈ 10^{-52} [/itex], which corresponds to the classical 60 e-foldings.

Prof. Susskind states here:

that 1000 e-foldings could work equally well. I cannot understand, why this is the case, since [itex] T_e [/itex] cannot get any arbitrary values.

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