The debate about the value of present Hubble parameter H_0 has heated up recent years with more precise measurements of different techniques. The standard candle measurements at low redshift (e.g., supernovae) yield an H_0 value of 74.0+-1.5 km/s/Mpc, while the standard ruler measurements at high redshift (e.g., cosmic microwave background) give an H_0 of 67.5+-0.5 km/s/Mpc. The tension is beyond 4.4σ. Currently, one approach to alleviate the tension is to modify the equation of state of the dark energy around the recombination so that the evolution of the Universe is changed accordingly, such as generalized proca theory.
We investigate the cosmological viability of the generalized proca theory and 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 and other late-time data sets (BAO, RSD, etc.) we show that the tension is reduced, as the 2 sigma allowed region for H_0 in Proca, H_0 = 70.4+0.94-0.87, overlaps with the 2sigma region of the HST data.