A Dark Energy model from Generalized Proca Theory

We consider a specific dark energy model, which only includes the Lagrangian up to the cubic order in terms of the vector field self-interactions in the generalized Proca theory. We examine the cosmological parameters in the model by using the data sets of CMB and CMB+HST, respectively. In particular, the Hubble constant is found to be $H_0=71.80_{-0.72}^{+1.07}$ ($72.48_{-0.60}^{+0.72}$) $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$ at $68\mathrm{\%}$~C.L. with CMB (CMB+HST), which would alleviate the Hubble constant tension. We also obtain that the reduced ${\chi }^2$ values in our model are close to unity when fitting with CMB and CMB+HST, illustrating that our model is a good candidate to describe the cosmological evolutions of the universe.