Big Bang Nucleosynthesis constraints on Barrow entropy

TL;DR

This paper uses Big Bang Nucleosynthesis data to constrain the quantum-gravitational parameter in Barrow entropy, finding that deviations from standard entropy must be very small to be consistent with early universe observations.

Contribution

It provides the first detailed BBN-based constraints on the Barrow entropy parameter, linking quantum-gravitational effects to cosmological observations.

Findings

Barrow entropy modifies Friedmann equations with extra terms.

The deviation in freeze-out temperature constrains the Barrow parameter.

Upper bound on the Barrow exponent is approximately 1.4×10^{-4}.

Abstract

We use Big Bang Nucleosynthesis (BBN) data in order to impose constraints on the exponent of Barrow entropy. The latter is an extended entropy relation arising from the incorporation of quantum-gravitational effects on the black-hole structure, parameterized effectively by the new parameter $\Delta$. When considered in a cosmological framework and under the light of the gravity-thermodynamics conjecture, Barrow entropy leads to modified cosmological scenarios whose Friedmann equations contain extra terms. We perform a detailed analysis of the BBN era and we calculate the deviation of the freeze-out temperature comparing to the result of standard cosmology. We use the observationally determined bound on $ |\frac{\delta {T}_f}{{T}_f}|$ in order to extract the upper bound on $\Delta$. As we find, the Barrow exponent should be inside the bound $\Delta\lesssim 1.4\times 10^{-4}$ in order not to spoil the BBN epoch, which shows that the deformation from standard Bekenstein-Hawking expression should be small as expected.