Test of Barrow entropy using a model independent approach

TL;DR

This paper tests the Barrow entropy model by linking quantum-gravitational effects to observable cosmological parameters, proposing a model-independent way to constrain the deformation parameter using current and future data.

Contribution

It introduces a relation between Barrow entropy deformation and curvature parameters, enabling observational constraints without relying on specific models.

Findings

Derived a formula connecting quantum deformation parameter with curvature parameters.

Predicted a slight deviation of the third derivative of scale factor from standard cosmology.

Proposed observational methods to test the Barrow entropy model using current and future data.

Abstract

Taking into consideration of a fractal structure for the black hole horizon, Barrow argued that the area law of entropy get modified due to quantum-gravitational effects. Accordingly, the corrected entropy takes the form $S\sim A^{1+\frac{\Delta}{2}}$, where $0\leq\Delta\leq1,$ indicates the amount of the quantum-gravitational deformation effects. By considering the modified Barrow entropy associated with the apparent horizon, the Friedmann equations get modified as well. We show that considering a universe filled with the matter and cosmological constant $\Lambda$, it is possible to determine the amount of deviation from standard cosmology by reconstructing the parameter $\delta$ in terms of curvature parameters $\{q,Q,\Omega_{k}\}$ as $\Delta=\frac{(Q-1-\Omega_k)(1+\Omega_k)}{(1+\Omega_k+q)^{2}}$. Here, $q$ is the deceleration parameter and $Q$ is the third derivative of scale factor . This relation provides some advantages. The first is that it indicates that there is profound connection between quantum-gravitational deformation effects and curvature effects, for $\Omega_k\simeq0$ the pair $\{q,Q\}$ can be regarded as deviation curvature factors which reflect the amount of deviation of the model from the standard model. The second interesting feature is that, since this pair are observational parameters which can be directly measured in a model independent approach, they can be regarded as powerful tools to enable us to put constraint on parameter $\Delta$ and test the Barrow entropy model. Our analysis predicts the value for $Q_{0}$ which is slightly deviates from 1 as $(Q_{0}-1)<0.001$. This can be a relativity well target and criterion for theoretical and observational measurements of parameter $Q_{0}$. Hence we can hope and wait the improvement of the high redshift data in the future to support it.