Constraints on R\'{e}nyi Entropy through Primordial Big-Bang Nucleosynthesis and Baryogenesis

TL;DR

This paper investigates how Rényi entropy modifies early universe expansion, constrains its parameters using primordial element abundances and baryogenesis data, and explores its potential to resolve the Lithium problem in cosmology.

Contribution

It derives modified Friedmann equations from Rényi entropy and provides the first systematic constraints on Rényi cosmology from Big-Bang Nucleosynthesis data.

Findings

Overlapping Rényi parameter ranges for Helium-4 and Deuterium.

Discrepancy in Rényi parameter ranges for Lithium-7.

Potential alleviation of the Lithium problem in modified cosmology.

Abstract

The R\'{e}nyi entropy, a one-parameter generalization of Boltzmann-Gibbs entropy, offers a promising framework for probing quantum gravitational effects in cosmology. By modifying the entropy-area relation of the apparent horizon, R\'{e}nyi entropy can alter the expansion dynamics of the early universe, with potential implications for Big-Bang Nucleosynthesis. In this work, we derive the modified Friedmann equations within the R\'{e}nyi entropy paradigm and investigate their impact on the primordial abundances of light elements Deuterium ($D$), Helium-4 ($_{}^{4}\textit{He}$), Lithium-7 ($_{}^{7}\textit{Li}$) and baryogenesis. Using observational constraints from Planck, primordial abundance data and observational data on baryogenesis, we put stringent bounds on the R\'{e}nyi parameter. Furthermore, we explore whether R\'{e}nyi entropy corrections could mitigate the long-standing Lithium discrepancy. This study provides the first systematic constraints on R\'{e}nyi cosmology from BBN and highlights the role of nonextensive thermodynamics in early-universe physics. Our analysis shows that the obtained ranges for the R\'{e}nyi parameter $\lambda$ exhibit a overlap for the Helium-4 and Deuterium, but this overlapping region-despite a small discrepancy-is inconsistent with the range obtained from Lithium-7. This small mismatch between the ranges raises the possibility of alleviating the \textit{Lithium Problem} in the modified cosmology scenarios. Furthermore, we present the relationship between the cosmic time and temperature within the framework of R\'{e}nyi cosmology. We observe that an increase in the R\'{e}nyi parameter increase the temperature of the early universe.