Reducing the $H_{0}$ tension with generalized Proca theory

We investigate the cosmological viability of the generalized proca theory. We first implement the background and linear perturbation equations of motion in the Boltzmann code and then study the constraints on the parameters of the generalized proca theory after running MCMC against the cosmological data set. With Planck + HST data, we obtain the constraint $h=0.7334_{-0.0269}^{+0.0246}$, which indicates that the tension between early universe and late time universe within this theory is removed. By adding other late-time data sets (BAO, RSD, etc.) we show that the tension is reduced, as the 2$\sigma$ allowed region for $h$ in Proca, $h=0.7041_{-0.0087}^{+0.0094}$, overlaps with the 2$\sigma$ region of the HST data.