Hubble Tension in Power-Law f(R) Gravity and Generalized Brans-Dicke Theory

TL;DR

This paper proposes a theoretical framework using scalar fields in Brans-Dicke and f(R) gravity theories to address the Hubble tension, showing that H0 evolves with redshift and is better alleviated by Brans-Dicke with exponential potential.

Contribution

It introduces a unified dynamical approach to interpret the Hubble tension within scalar-tensor theories, highlighting the effectiveness of Brans-Dicke with exponential potential.

Findings

H0 evolves with redshift, matching local and CMB measurements.

Brans-Dicke with exponential potential better relieves Hubble tension.

Power-law f(R) gravity is less successful in addressing the tension.

Abstract

We introduce a theoretical framework to alleviate the Hubble tension. This framework is based on dynamics of a minimally coupled scalar field which either belongs to the Brans-Dicke theory with a self-interacting potential or is the scalar partner of f(R) gravity. These two theories are dynamically equivalent when the Brans-Dicke parameter is zero. We will use this dynamical equivalence to interpret the Hubble tension in the same theoretical framework. For both theories, we write one set of field equations in which the value of a parameter distinguishes between the two theories. We will show that H0 actually evolves with redshift so that its value is consistent with that measured from the local distance ladder and it drops to the value measured from CMB at high redshift. We argue that even though both theories exhibit this behaviour, Brans-Dicke theory with an exponential potential is more successful than power-law f(R) gravity to relieve the Hubble tension.