Impact of the latest measurement of Hubble constant on constraining inflation models

Abstract: We investigate how the constraint results of inflation models are affected by considering the latest local measurement of $H_0$ in the global fit. We use the observational data, including the Planck CMB full data, the BICEP2 and Keck Array CMB B-mode data, the BAO data, and the latest measurement of Hubble constant, to constrain the $\Lambda$CDM+$r$+$N_{\rm eff}$ model, and the obtained 1$\sigma$ and 2$\sigma$ contours of $(n_s, r)$ are compared to the theoretical predictions of selected inflationary models. We find that, in this fit, the scale invariance is only excluded at the 3.3$\sigma$ level, and $\Delta N_{\rm eff}>0$ is favored at the 1.6$\sigma$ level. The natural inflation model is now excluded at more than 2$\sigma$ level; the Starobinsky $R^2$ model becomes only favored at around 2$\sigma$ level; the most favored model becomes the spontaneously broken SUSY inflation model; and, the brane inflation model is also well consistent with the current data, in this case.