Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence

TL;DR

This paper explores how logarithmic quantum gravity corrections influence early-universe cosmology within a varying-G framework, revealing conditions for inflation and potential solutions to cosmological singularities.

Contribution

It introduces the application of the GEVAG framework to analyze logarithmic entropy corrections, highlighting their effects on early-time cosmology and inflation.

Findings

Negative correction coefficient doubles effective G

Positive coefficient supports natural slow-roll inflation

GEVAG approach can avoid sudden singularities

Abstract

According to the GEVAG (Generalized Entropy Varying-G) framework, any modification to the Bekenstein-Hawking area law would also lead to a varying-$G$ gravity theory in which the effective gravitational constant $G_\text{eff}$ becomes area-dependent. Among a myriad of generalized entropy functions explored in the literature, of special interest is the logarithmic correction of quantum gravity. In this work, we apply GEVAG to investigate the effect of logarithmic correction on very early-time cosmology, including the conditions for inflation. We found that if the coefficient of the logarithmic correction term is negative, $G_\text{eff}$ becomes twice that of the current value; whereas, a positive coefficient leads to a very small value of $G_\text{eff}$, which may ameliorate the "arrow of time" problem. In fact, slow-roll inflation becomes more natural in the latter case. We make some comparisons with the constant-$G$ approach and reveal the advantages of the GEVAG approach. For example, it can evade the sudden singularity that could otherwise arise when the coefficient of the logarithmic correction term is negative. We also check the validity of the generalized second law and comment on the range of the various parameters.