  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.
