Big Bang Nucleosynthesis and Entropy Evolution in $f(R,T)$ Gravity

The present article is devoted to constrain the model parameter $χ$ for the $f(R,T)= R + χT$ gravity model by employing the constraints coming from big bang nucleosynthesis. We solve the field equations and constrain $χ$ in the range $-0.14 κ^{2} \leq χ\leq 0.84 κ^{2}$ (where $κ^{2} = \frac{8 πG}{c^{4}}$) from the primordial abundances of light elements such as helium-4, deuterium and lithium-7. We found the abundances of helium-4 and deuterium agrees with theoretical predictions, however the lithium problem persists for the $f(R,T)$ gravity model. We also investigate the evolution of entropy for the constrained parameter space of $χ$ for the radiation and dust universe. We report that entropy is constant when $χ= 0$ for the radiation dominated universe, whereas for the dust universe, entropy increases with time. We finally use the constraints to show that $χ$ has negligible influence on the cold dark matter annihilation cross section.

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