Inflation model selection revisited after a 1.91% measurement of the Hubble constant

Abstract: The recent local measurement of the Hubble constant based on the distance-ladder method has reached a $1.91\%$ precision, but this result is in tension with the early-universe measurements at the more than 4$\sigma$ level, bringing a crisis to the contemporary cosmology. In addition to the end-to-end test of the $\Lambda$CDM model in the late universe, it is also of great interest to see how the local $H_0$ measurement affects the determination of the primordial power spectra, and further to test the influences for the inflation model selection. Here, we constrain the primordial power spectra of scalar and tensor perturbations by using a series of observational data, including the Planck 2015 cosmic microwave background (CMB) temperature and polarization power spectra data, the Planck 2018 lensing power spectrum data, the BICEP2/Keck Array CMB B-mode data, and also the prior of optical depth $\tau=0.054\pm0.007$, as well as the late-universe measurements (baryon acoustic oscillations and type Ia supernovae). In particular, we use the latest $1.91\%$ measurement of the Hubble constant, $H_{0}=74.03\pm1.42$ km s$^{-1}$ Mpc$^{-1}$, in this cosmological test. We find that considering the latest local $H_{0}$ measurement in the data combination will lead to a larger fit value of $n_{\rm s}$. With the addition of the latest local measurement of $H_{0}$, it is found that the natural inflation model is totally excluded at the $2\sigma$ level, the Starobinsky $R^{2}$ inflation model is marginally favored at around the $2\sigma$ level, and the spontaneously broken SUSY inflation model is the most favored model.