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

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.