galOperon

Late-time entropy production from scalar decay and the relic neutrino temperature

“…We assume that when the neutrinos decouple, ρ φ ≪ ρ R , such that ρ φ /ρ R cannot be neglected, but its higher powers can. It is possible to show [12], in fact, that decoupling is not possible when ρ φ ≫ ρ R . In the era ρ φ ≪ ρ R of incomplete radiation domination, the Friedmann equation is put in the form…”

“…In (10), the exponential will dominate at the epochs i and f , and in between, when ρ R ≫ ρ φ . So, in the pre-exponential, we may approximate T from ( 6) using the full radiation domination equations H = 1/(2t) and H 2 = 8πρ R /(3M 2 P l ).…”

“…Estimate of Φ E Because there are as yet no firm phenomenological values for Φ E , we have to make an estimate. In the expression for Ṡ given in (10), the exponential dominates at the epochs we are interested in. So, we estimate Φ E in the pre-exponential just to an order of magnitude, defining the epoch E by taking ρ R = ρ φ at t = t E .…”

“…However, we will approximate T E in ( 14), i.e. in the pre-exponential of (10), by putting x = x E ≈ 1 for t = t E in (24). Now, ( 19) and ( 23) signify that our approximations are equivalent to taking ρ Φ = ρ R when Γ = H, to an order of magnitude, in the correction term in H 2 , and this is our way of bypassing lack of knowledge about the initial value of Φ.…”

“…The effect on neutrino decoupling and nucleosynthesis has been studied [7,8,9,10]. The studies do not depend materially on the details of flaton phenomenology, and apply to the Mev-scale decay of any scalar φ.…”