Extra Relativistic Species at a Bounce: The Minimum Delta N eff Imposed by a Capped Thermal History

At the largest Standard Model value, g_* = 106.75, the floors are 2.68e-02 for a scalar, 4.69e-02 for a Weyl fermion and 5.35e-02 for a vector. A scalar that instead stayed coupled until the MeV era would contribute 5.71e-01, more than twenty times its floor. Against the adopted Planck ceiling of 3.00e-01, the universe can hide at most about 11.2 scalars or 6.4 Weyl fermions if every one of them decouples at the highest temperatures. The bounce temperature corresponding to the bound density of 9.72e+54 g per cubic centimetre is 2.82e+18 eV, far above the electroweak scale, so the full Standard Model g_* is indeed traversed on the way down. This study is computed from stated assumptions and published comparison values; it is not a measurement.