Big Bang nucleosynthesis and baryogenesis in power-law f(R) gravity: Revised constraints from the semianalytical approach

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In this paper we investigate the primordial nucleosynthesis in L=ε²⁻²βRβ+16πmₚ⁻²Lₘ gravity, where ε is a constant balancing the dimension of the field equation, and 1<β<(4+√6)/5 for the positivity of energy density and temperature. From the semianalytical approach, the influences of β to the decoupling of neutrinos, the freeze-out temperature and concentration of nucleons, the opening of deuterium bottleneck, and the ⁴He abundance are all extensively analyzed; then β is constrained to 1<β<1.05 for ε=1 [1/s] and 1<β<1.001 for ε=mₚ (Planck mass). Supplementarily from the empirical approach, abundances of the lightest elements (D, ⁴He, ⁷Li) are computed by the model-independent best-fit formulae for nonstandard primordial nucleosynthesis, and we find the constraint 1< β≤ 1.0505 which corresponds to the extra number of neutrino species 0< ΔNνeff ≤ 0.6365; also, the ⁷Li abundance problem cannot be solved by L=ε²⁻²βRβ+16πmₚ⁻²Lₘ gravity for this domains of β. Finally, the consistency with the mechanism of gravitational baryogenesis is estimated.