Renyi Entropy Correction to Expanding Universe

TL;DR

This paper derives modified Friedmann equations for an expanding universe by applying Renyi entropy corrections to the apparent horizon, linking quantum effects, thermodynamics, and cosmological dynamics.

Contribution

It introduces a novel approach using Renyi entropy to modify the thermodynamics of the universe, leading to new cosmological equations.

Findings

Derived corrections to Newton's law of gravitation.

Obtained modified Friedmann equations for the universe.

Examined the second law of thermodynamics in this context.

Abstract

The Renyi entropy coprises a group of data estimates that sums up the well-known Shannon entropy, acquiring a considerable lot of its properties. It appears as unqualified and restrictive entropy, relative entropy, or common data, and has found numerous applications in information theory. in the Renyi's argument, the area law of the black hole entropy plays a significant role. However, the total entropy can be modified by some quantum effects, motivated by the randomness of a system. In this note, by employing this modified entropy relation, we have derived corrections to Newton's law of gravitation. Taking this entropy associated with the apparent horizon of the Friedmann-Robertson-Walker Universe and assuming the first law of thermodynamics, dE=TdS+WdV, satisfies the apparent horizon, we have reconsidered expanding Universe and find modified Friedmann equations. Also, the second thermodynamics law has been examined.