Alleviating $H_0$ Tension with New Gravitational Scalar Tensor Theories

We investigate the cosmological applications of new gravitational scalar-tensor theories and we analyze them in the light of $H_0$ tension. In these theories the Lagrangian contains the Ricci scalar and its first and second derivatives in a specific combination that makes them free of ghosts, thus corresponding to healthy bi-scalar extensions of general relativity. We examine two specific models, and for particular choices of the model parameters we find that the effect of the additional terms is negligible at high redshifts, obtaining a coincidence with $\Lambda$CDM cosmology, however as time passes the deviation increases and thus at low redshifts the Hubble parameter acquires increased values ($H_0\approx 74 km/s/Mpc$) in a controlled way. The mechanism behind this behavior is the fact that the effective dark-energy equation-of-state parameter exhibits phantom behavior, which implies faster expansion, which is one of the theoretical requirements that are capable of alleviating the $H_0$ tension. Lastly, we confront the models with Cosmic Chronometer (CC) data showing full agreement within 1$\sigma$ confidence level.