The implications of inflation for the last ACT

We explored a parameterized slow-roll inflationary model within the $\Lambda$CDM framework, utilizing a combination of data from Planck 2018, ACT DR6, DESI DR2, and BICEP/Keck 2018 (P-ACT-LB-BK18). Additionally, we incorporated the SH0ES prior on $H_0$ (P-ACT-LB-BK18-$H_0$) to analyze the model within the early dark energy (EDE) framework. While the model with a potential $V(\phi)\propto \phi^\alpha$ for small values of $\alpha$ still fits the data, the Starobinsky $R^2$ inflation falls outside the $2\sigma$ region. On the other hand, in a self-consistent quantum theory of gravity, higher-order corrections to $R$ are typically anticipated. In response, we proposed a non-perturbative exponential $f(R)$ inflation model, wherein the subleading corrections beyond $R^2$ including terms like $R^3$ or $R^4$. Using numerical calculations and Markov Chain Monte Carlo (MCMC) analysis with the P-ACT-LB-BK18 data set, we demonstrate that this model can align well with the ACT-preferred value of the scalar spectral index. Additionally, within the early dark energy (EDE) framework, it accommodates greater deviations from the original Starobinsky $R^2$ inflation model when incorporating the SH0ES prior on $H_0$.