Barrow Cosmology and Big-Bang Nucleosynthesis

TL;DR

This paper explores how Barrow entropy modifies Friedmann equations and constrains the Barrow exponent using Big-Bang Nucleosynthesis data, finding that deviations from standard cosmology are minimal.

Contribution

It provides a formal derivation of modified Friedmann equations based on Barrow entropy and constrains the Barrow exponent using observational BBN data.

Findings

Barrow parameter $oldsymbol{\delta hickapprox 0.01}$ is consistent with BBN constraints.

Deviation from standard cosmology due to Barrow entropy is small.

Early universe temperature increases with the Barrow exponent $oldsymbol{\delta}$.

Abstract

Using thermodynamics-gravity conjecture, we present the formal derivation of the modified Friedmann equations inspired by the Barrow entropy, $S\sim A ^{1+\delta/2}$, where $0\leq\delta\leq 1$ is the Barrow exponent and $A$ is the horizon area. We then constrain the exponent $\delta$ by using Big-Bang Nucleosynthesis (BBN) observational data. In order to impose the upper bound on the Barrow exponent $\delta$, we set the observational bound on $\left| \frac{\delta T_f} {T_f }\right|$. We find out that the Barrow parameter $\delta$ should be around $ \delta \simeq 0.01$ in order not to spoil the BBN era. Next we derive the bound on the Barrow exponent $\delta$ in a different approach in which we analyze the effects of Barrow cosmology on the primordial abundances of light elements i.e. Helium $_{}^{4}\textit{He}$, Deuterium $D$ and Lithium $_{}^{7}\textit{Li}$. We observe that the deviation from standard Bekenstein-Hawking expression is small as expected. Additionally we present the relation between cosmic time $t$ and temperature $T$ in the context of modified Barrow cosmology. We confirm that the temperature of the early universe increases as the Barrow exponent $\delta$ (fractal structure of the horizon) increases, too.