The implications of inflation for the last ACT

We explored a parameterized slow-roll inflationary model within the ΛCDM 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 H₀ (P-ACT-LB-BK18-H₀) to analyze the model within the early dark energy (EDE) framework. While the model with a potential V(ϕ) ∝ ϕ^α for small values of α still fits the data, the Starobinsky R² inflation falls outside the 2σ 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 R² including terms like R³ or R⁴. 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 EDE framework, it accommodates greater deviations from the original Starobinsky R² inflation model when incorporating the SH0ES prior on H₀.