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

Abstract

In this paper we investigate the primordial nucleosynthesis in $\mathcal{L}={\epsilon }^{2-2\beta }{R}^{\beta }+16\pi m_P^{-2}{\mathcal{L}}_m$ gravity, where $\epsilon$ is a constant balancing the dimension of the field equation, and $1<\beta <(4+\sqrt{6})/5$ for the positivity of energy density and temperature. From the semianalytical approach, the influences of $\beta$ to the decoupling of neutrinos, the freeze-out temperature and concentration of nucleons, the opening of deuterium bottleneck, and the ${}^4$He abundance are all extensively analyzed; then $\beta$ is constrained to $1<\beta <1.05$ for $\epsilon =1$ [1/s] and $1<\beta <1.001$ for $\epsilon =m_P$ (Planck mass). Supplementarily from the empirical approach, abundances of the lightest elements (D, ${}^4$He, ${}^7$Li) are computed by the model-independent best-fit formulae for nonstandard primordial nucleosynthesis, and we find the constraint $1<\beta \le 1.0505$ which corresponds to the extra number of neutrino species $0<\Delta N_{\nu }^{\text{eff}}\le 0.6365$; also, the ${}^7$Li abundance problem cannot be solved by $\mathcal{L}={\epsilon }^{2-2\beta }{R}^{\beta }+16\pi m_P^{-2}{\mathcal{L}}_m$ gravity for this domains of $\beta$. Finally, the consistency with the mechanism of gravitational baryogenesis is estimated.

Comments: 7 Figures, 2 numerical tables