Late-time acceleration due to a generic modification of gravity and the Hubble tension

We consider a scenario of modified gravity, which is generic to late-time acceleration, namely, acceleration in the Jordan frame and no Einstein frame. The possibility realized by assuming an interaction between dark matter baryonic component removed going using disformal transformation giving rise exotic effective fluid responsible for causing phantom crossing at late times. In this scenario, past evolution not distinguished from $\Lambda$CDM but time dynamics generically different due presence that causes monotonous increase expansion rate distinctive cosmic feature. latter can play crucial role addressing tension observed value Hubble parameter CMB (Cosmic Microwave Background) measurements local observations. demonstrate significantly reduces under consideration chosen scale factor parametrizations. estimated age universe model well within observational bounds low high red-shift regimes.