“…This is the case, for example, setting the experimental inputs as in Sec. 6.1 and the values of the other parameters as follows: M 1 = 10 11 GeV, M 2 = 6.4 × 10 13 GeV, 6 A simple formula for T a dec was proposed by [70] T a dec 9.6 × 10 6 GeV f a 10 10 GeV We observe that this formula gives a T a dec always below f a as long as f a 10 12 GeV, which is required in order not to overproduce dark matter [22]. M 3 > MPl , f a 5 × 10 10 GeV, λ HA (M A ) 0.016, λ A (M A ) 0.10, y(M A ) = 0.1, ξ H (M A ) 14 and ξ A (M A ) −2.6.…”