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

TL;DR

This paper explores how a specific power-law f(R) gravity model affects primordial nucleosynthesis, constraining model parameters using semianalytical and empirical methods, and assesses implications for baryogenesis and the lithium problem.

Contribution

It provides new constraints on the power-law index in f(R) gravity from nucleosynthesis data and analyzes its impact on early universe processes and baryogenesis.

Findings

Constrained the parameter β to 1<β<1.05 for ε=1/s and 1<β<1.001 for ε=m_P.

Found the element abundances consistent with β up to 1.0505, corresponding to ΔN_ν^eff ≤ 0.6365.

Showed that the lithium problem cannot be solved within this f(R) gravity model.

Abstract

In this paper we investigate the primordial nucleosynthesis in $\mathscr{L}=\varepsilon^{2-2\beta}R^\beta+{16\pi}m_P^{-2}\mathscr{L}_m$ gravity, where $\varepsilon$ 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 $\varepsilon=1$ [1/s] and $1<\beta<1.001$ for $\varepsilon=m_P$ (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 $1< \beta \leq 1.0505$ which corresponds to the extra number of neutrino species $0< \Delta N_\nu^{\text{eff}} \leq 0.6365$; also, the $^7$Li abundance problem cannot be solved by $\mathscr{L}=\varepsilon^{2-2\beta}R^\beta+{16\pi}m_P^{-2}\mathscr{L}_m$ gravity for this domains of $\beta$. Finally, the consistency with the mechanism of gravitational baryogenesis is estimated.