Constraints on Attractor Models of Inflation and Reheating from Planck, BICEP/Keck, ACT DR6, and SPT-3G Data

Abstract

We analyze the latest cosmic microwave background (CMB) constraints on the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from Planck 2018, BICEP/Keck 2018, the Atacama Cosmology Telescope Data Release 6 (ACT DR6), and the South Pole Telescope (SPT-3G) data, focusing on their implications for attractor models of inflation. We compare systematically observational bounds with theoretical predictions for both E-model ($\alpha$-Starobinsky) and T-model potentials. The observational constraints accommodate E-models with $\alpha \lesssim 25$, with the canonical Starobinsky model ($\alpha = 1$) predicting $n_s = 0.958-0.963$ for reheating temperatures between $100 - 10^{10}$ GeV, in good agreement with Planck 2018 data and within the 95% CL region determined by the Planck-ACT-SPT combination, but below the 95% confidence region of the Planck-ACT-DESI combination. Higher reheating temperatures from near-instantaneous reheating improve the compatibility. T-models predict slightly lower $n_s$ values (0.956-0.961), in some tension with Planck 2018 data, and we find an upper limit of $\alpha \lesssim 11$ in these models. We extend our analysis to generalized $\alpha$-attractors with monomial potentials $V(\varphi) \propto \varphi^k$ near the minimum, demonstrating that models with $k \geq 6$ naturally predict $n_s \simeq 0.965 - 0.968$ for typical number of $e$-folds, in better agreement with the ACT DR6 data. We also consider deformed E- and T-models, which allow significantly higher values of $n_s$ for low values of $\alpha \simeq 1$.