Generalized Brans-Dicke theory from Verlinde's entropic gravity

TL;DR

This paper introduces a q-deformed scalar-tensor gravity model combining Verlinde's entropic gravity with deformation effects, resulting in a generalized Brans-Dicke framework that recovers standard models in certain limits.

Contribution

It develops a novel q-deformed scalar-tensor theory of gravity based on entropic principles, extending Brans-Dicke theory with a deformation function.

Findings

The model modifies the Brans-Dicke framework via a deformation function.

The q-deformed field equations are consistent and recover standard gravity in specific limits.

The formulation preserves key symmetries and offers a generalized gravitational dynamics description.

Abstract

In this work, we develop a q-deformed scalar-tensor theory of gravitation by combining Verlinde's entropic gravity paradigm with statistical deformation effects. The resulting model modifies the Brans-Dicke framework through a deformation function, treated as a constant rescaling factor for the effective gravitational coupling. We derive the corresponding q-deformed field equations and analyze their theoretical consistency including the recovery of standard gravitational models in specific limits. While the present formulation preserves key symmetries and provides a generalized description of gravitational dynamics, it does not yield a significant deviation from Brans-Dicke theory. The study concludes with prospects for future research, including the exploration of cosmological solutions arising from the q-deformed field equations.