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

TL;DR

This paper evaluates how current CMB data constrain attractor inflation models, particularly E- and T-models, and explores their compatibility with observational bounds, including effects of reheating temperatures and generalized potentials.

Contribution

It systematically compares observational bounds with theoretical predictions for attractor inflation models, extending analysis to generalized and deformed models with new constraints.

Findings

E-models with $ ext{alpha} extless 25$ are compatible with data

Starobinsky model ($ ext{alpha}=1$) fits well with Planck 2018

Higher reheating temperatures improve model-data agreement

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 $\alpha \simeq 1$.