Big-Bang Nucleosynthesis and WIMP Dark Matter Freeze-Out as Probes of Yukawa Cosmology

Abstract

We investigate Big-Bang Nucleosynthesis (BBN) in the context of Yukawa cosmology. We first derive the modified Friedmann equations by starting from the first law of thermodynamics on the apparent horizon. Using observational data on \(^4\mathrm{He}\), deuterium, and \(^7\mathrm{Li}\) abundances, we place stringent bounds on the Yukawa coupling \(α\). The \(^4\mathrm{He}\) and deuterium constraints are mutually consistent (\(-0.24 \lesssim α\lesssim 0.12\)), while \(^7\mathrm{Li}\) requires $α\in [-0.76,\,-0.72]$. This indicate that Yukawa cosmology cannot resolve the Lithium Problem. We then extend our analysis to WIMP freeze-out, and show that the modified Hubble parameter alters the relic abundance, yielding an independent constraint \(-0.017 \lesssim α\lesssim 0.018\) from \(Ω_{\mathrm{CDM}}h^2 = 0.120 \pm 0.001\). We also derive the modified time-temperature relation, and show that the positive \(α\) raises the early Universe temperature. Our analysis demonstrates that BBN and dark matter relic abundance serve as complementary probes of modified gravity. Our studies confirm that Yukawa cosmology is a testable framework for early-Universe physics.