Metric $f(R)$ gravity with dynamical dark energy as a scenario for the Hubble tension

Abstract: We introduce a theoretical framework to interpret the Hubble tension, based on the combination of a metric $f(R)$ gravity with a dynamical dark energy contribution. The modified gravity provides the non-minimally coupled scalar field responsible for the proper scaling of the Hubble constant, in order to accommodate for the local SNIa pantheon+ data and Planck measurements. The dynamical dark energy source, which exhibits a phantom divide line separating the low red-shift quintessence regime ($-1<w<-1/3$) from the phantom contribution ($w<-1$) in the early Universe, guarantees the absence of tachyonic instabilities at low red-shift. The resulting $H_0(z)$ profile rapidly approaches the Planck value, with a plateau behaviour for $z\gtrsim 5$. In this scenario, the Hubble tension emerges as a low red-shift effect, which can be in principle tested by comparing SNIa predictions with far sources, like QUASARS and Gamma Ray Bursts.