Heavy Field Effects on Inflationary Models in Light of ACT Data

TL;DR

This work investigates how a heavy scalar field with mass $m\sim H$ and a sizable mixing $ρ$ to the inflaton alters inflationary observables through a single-field EFT with a reduced sound speed $c_s(m/H,ρ/H)$. The authors show that in the strong-mixing regime, $n_s$ and $α_s$ can increase, allowing Starobinsky-type, chaotic, and natural inflation to fit ACT data that challenge the traditional models, and they quantify these changes via updated expressions for $P_ζ$, $n_s$, $r$, and $α_s$. They also analyze the enhanced non-Gaussianity, deriving an equilateral form for $f_{NL}^{eq}$ and discussing cosmological collider signals that could reveal the heavy field through oscillations in the squeezed limit; they further present two-field realizations with axionic couplings that realize large turning. The results provide a concrete pathway to reconciling current CMB constraints with a broader class of inflationary models and offer observable signatures—non-Gaussianity and collider-like oscillations—that can be tested with future data and multi-field UV completions.

Abstract

Recent results from the Atacama Cosmology Telescope (ACT), when combined with Planck and DESI datasets, indicate a scalar spectral index $n_s$ larger than that reported in the Planck 2018 baseline, thereby challenging conventional Starobinsky-type ($α$-attractor) inflationary scenarios at the $2σ$ level. In addition, the positive running of the spectral index $α_s$ implied by the data provides strong constraints on these models. In this paper, we explore the possibility that the presence of an additional heavy field during inflation, with a mass of order the Hubble scale and a sizable mixing coupling to the inflaton, can reconcile such inflationary models with the ACT results by increasing both $n_s$ and $α_s$, particularly in the strong-mixing regime. Furthermore, we extend this framework to traditional inflation models such as chaotic inflation and natural inflation, which have already been excluded by Planck alone, and show that they can be revived in certain regions of parameter space. Inflationary observables, including the spectral index $n_s$, the tensor-to-scalar ratio $r$, and the running $α_s$, are computed within the single-field EFT approach, which is applicable even in the presence of a heavy field with large mixing. We also discuss the non-Gaussianity signatures arising from the heavy field, noting that parts of the parameter space are already excluded or can be tested in future observations. Finally, we present concrete model realizations that allow for such a large mixing.

Figures (12)

• Figure 1: Inflationary predictions in Starobinsky inflation with an additional field of mass $m$ and mixing coupling $\rho$. Left : $(n_s,r)$ plane obtained by varying $\rho$ while fixing $m$ as indicated in the panel. Solid (dashed) curves correspond to $N=60$ ($N=50$). Along each curve, $\rho/H$ is varied from $\rho_{\rm min}$ to $\rho_{\mathrm{max}}$, with markers at the edge $\blacktriangle$ and $\blacksquare$ denoting $\rho_{\rm min}$ and $\rho_{\mathrm{max}}$, respectively. Here $\rho_{\rm min}$ is chosen as the minimal value of $\rho$ consistent with the validity of the EFT description, $m^2+\rho^2>4H^2$, whereas $\rho_{\mathrm{max}}$ is fixed as $\rho_{\mathrm{max}}/H= 61,64,66,68,77,89$ for $m/H=1,\sqrt{2},\sqrt{3},2,3,4$ to be consistent with the Planck constraints on the equilateral non-Gaussianity, $f_{\mathrm{NL}}^{\mathrm{eq}}=-26\pm 47$Planck:2019kim, as discussed later in Sec. \ref{['sec:NG']}. The constraints on $(n_s,r)$ are derived from the combined Planck, ACT, and DESI data set (P-ACT-LB-BK18), with dark and light purple regions corresponding to the $1\sigma$ and $2\sigma$ confidence levels, respectively. The constraints from Planck-LB-BK18 are shown in dark and light orange. Right : $(n_s,\alpha_s)$ plane for the same parameter variation as in the left panel. The observational constraints are taken from Ref. ACT:2025tim, where Planck-only (orange), P-ACT (navy), and P-ACT-LB (purple) results are shown.
• Figure 2: The same format as the left panel of Fig. \ref{['fig1']}, but for chaotic inflation. From the upper left to the lower right, we show the $(n_s,r)$ plane for $n=\tfrac{1}{2},\,1,\,2,\,4$.
• Figure 3: The same format as the right panel of Fig. \ref{['fig1']}, but for chaotic inflation. From the upper left to the lower right, we show the $(\alpha_s,n_s)$ plane for $n=\tfrac{1}{2},\,1,\,2,\,4$.
• Figure 4: Same format as Fig. \ref{['fig1']}, but for natural inflation. For $m/H=5,10$, $\rho_{\mathrm{max}}$ is taken as $\rho_{\mathrm{max}}/H= 102,177$ to be consistent with bound on non-Gaussianity.
• Figure 5: Left: Contour plots of $n_s$ for $N=60$ as functions of $m/H$ and $\rho/H$ in Starobinsky inflation, chaotic inflation with $n=2$, and natural inflation with the axion decay constant $f=5$. The black (red) curve indicates the maximum (minimum) values of $n_s$ and $\alpha_s$ from Eq. \ref{['ACT']}. The region violating the EFT validity condition $m^2+\rho^2<4H^2$ is excluded from the figures. The gray region shows the bound from non-Gaussianity. Right: Contour plots of $\alpha_s$ with the same parameter variations as in the left panel.