Thermodynamic constraints on a varying cosmological-constant-like term from the holographic equipartition law with a power-law corrected entropy

TL;DR

This paper explores how a quantum entanglement-based power-law corrected entropy influences cosmological equations via holographic equipartition, constraining the extra driving term to align with observed cosmological constant values.

Contribution

It introduces a thermodynamic framework applying power-law corrected entropy to holographic equipartition, linking quantum corrections to cosmological acceleration.

Findings

The extra driving term is proportional to the Hubble parameter raised to the power of alpha.

Thermodynamic constraints limit the driving term to be consistent with observed cosmological constant.

The model predicts the driving term becomes nearly constant for small alpha.

Abstract

A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the $\alpha$-th power of the Hubble parameter, where $\alpha$ is a dimensionless constant for the power-law correction) in the acceleration equation, which can be derived from the holographic equipartition law. Interestingly, the value of the extra driving term in the present model is constrained by the second law of thermodynamics. From the thermodynamic constraint, the order of the driving term is found to be consistent with the order of the cosmological constant measured by observations. In addition, the driving term tends to be constant-like when $\alpha$ is small, i.e., when the deviation from the Bekenstein-Hawking entropy is small.