The implications of inflation for the last ACT

TL;DR

The paper addresses the tension between ACT DR6 observations and the Starobinsky $R^2$ inflation within $\Lambda$CDM, and explores whether higher-curvature corrections can restore compatibility when an SH0ES prior on $H_0$ is included via an early dark energy (EDE) framework. It employs two complementary analyses: (i) a parameterized slow-roll model with $\epsilon(N) = \dfrac{c}{2 (N+\Delta N)^p}$ and corresponding $r$ and $n_s$ expressions, constrained by P-ACT-LB-BK18 and, in EDE, by P-ACT-LB-BK18-$H_0$; (ii) a non-perturbative exponential $f(R)$ model with $F(R) = \dfrac{R^2}{2\mu^2} \exp[-\lambda (R/\mu^2)^n]$, analyzed via the Einstein frame and MCMC. The results show that the $R^2$ point lies outside the $2\sigma$ region in both frameworks, while models with $V(\phi) \propto \phi^{\alpha}$ are viable for small $\alpha$, and that the exponential $f(R)$ extension with $\lambda>0$ can better accommodate the ACT-preferred $n_s$, with larger $\lambda$ favored in EDE. These findings suggest that non-perturbative higher-curvature corrections offer a promising path to reconcile inflation with current CMB data, and will be testable with upcoming CMB-S4, Simons Observatory, and LiteBIRD observations.

Abstract

We explored a parameterized slow-roll inflationary model within the $Λ$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 $V(φ)\propto φ^α$ for small values of $α$ still fits the data, the Starobinsky $R^2$ 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 $R^2$ 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 $H_0$.

Figures (4)

• Figure 1: The constraints on $c$ and $p$ within $\Lambda$CDM and EDE frameworks by adopting P-ACT-LB-BK18 and P-ACT-LB-BK18-$H_0$, respectively. Markers for $R^2$ inflation, D3-brane inflation and polynomial potential inflation are shown.
• Figure 2: The potential of $\phi$ .
• Figure 3: The predictions of the non-perturbative exponential $f(R)$ inflation model versus the constraints from P-ACT-LB-BK18 and P-ACT-LB-BK18-$H_0$ within the $\Lambda$CDM and EDE frameworks, respectively. Notably, the shaded region on the right of $R^2$ inflation line corresponds to $\lambda>0$, while the shaded region on the left corresponds to $\lambda<0$, which is strongly disfavored.
• Figure 4: Constraints on $\lambda$ for $n=1$ (solid line) and $n=2$ (dashed line) in the non-perturbative exponential $f(R)$ gravity inflation model by using P-ACT-LB-BK18 and P-ACT-LB-BK18-$H_0$ within the $\Lambda$CDM and EDE frameworks respectively.