Inflationary Models with Gauss-Bonnet Coupling in Light of ACT Observations

TL;DR

This work addresses the tension between ACT-based measurements and universal inflationary attractors by introducing a Gauss–Bonnet coupling with $\xi(\phi)=3\lambda/[4V(\phi)]$ that preserves $n_s$ (up to a field rescaling) while suppressing the tensor-to-scalar ratio by $r\to(1-\lambda)\,r$. By applying this mechanism to chaotic inflation, E- and T-models, and hilltop inflation, the authors identify broad parameter regions where predictions align with the latest P-ACT-LB constraints, notably for moderate $\lambda$ such as $\lambda=0.8$. The key result is that GB couplings can render a wide class of inflationary potentials compatible with current CMB data without heavily constraining $n_s$, effectively decoupling $r$ from model viability. The paper also discusses limitations (e.g., potential issues as $\lambda\to1$, need for higher-order corrections) and highlights future observations (LiteBIRD, CMB-S4) that will decisively test these GB-inflation scenarios.

Abstract

Recent analyses combining Atacama Cosmology Telescope (ACT) data with other cosmological datasets report a higher scalar spectral index $n_s$, creating tension with a wide range of inflationary models. Since a Gauss-Bonnet term with a coupling function $ξ(φ) = 3λ/[4V(φ)]$ leaves $n_s$ nearly unchanged (up to a field rescaling) while reducing the tensor-to-scalar ratio $r$ by a factor $(1-λ)$, so choosing $(1-λ)$ sufficiently small effectively removes $r$ as a limiting observable, making it easier for inflationary models to satisfy the latest observational constraints and alleviating this tension. Applying this mechanism to chaotic inflation, E-models, T-models, and hilltop inflation, we find that broad regions of parameter space become consistent with the latest ACT-based CMB constraints. These results demonstrate that Gauss-Bonnet couplings can help bring a broad class of inflationary models into agreement with current CMB measurements.

Figures (5)

• Figure 1: Constraints on chaotic inflation with a Gauss–Bonnet coupling for $N=60$. The blue and gray regions correspond to parameter values predicting $n_s$ and $r$ consistent with the $1\sigma$ and $2\sigma$ confidence regions from the P-ACT-LB-BK18 data, respectively. The P-ACT-LB-BK18 data are shown in Fig. \ref{['fig:comparison']}.
• Figure 2: Comparison between the model predictions and the observational data. The purple regions indicate the $1\sigma$ and $2\sigma$ confidence regions from the P-ACT-LB-BK18 data. Dashed curves correspond to inflationary models without Gauss-Bonnet coupling ($\lambda = 0$), while solid curves represent models with Gauss-Bonnet coupling with $\lambda = 0.8$. The black, blue, red, and green curves show the predictions from the chaotic inflation model, the E-model with $n = 1/2$, the T-model with $n = 1/2$, and the hilltop inflation model with $p = 4$, respectively. The red star and red dot indicate the predictions of the $p = 1$ chaotic inflation model with and without Gauss-Bonnet coupling, respectively. The figure illustrates how Gauss-Bonnet coupling shifts the model predictions toward the observationally favored region.
• Figure 3: Constraints on the parameters $n$ and $\tilde{\alpha}$ of the E-model, derived from the P-ACT-LB data as given in Eq. \ref{['act:constraints']}. The blue region corresponds to parameter values for which the predicted scalar spectral index given by Eq. \ref{['emodnseq1']} from the E-model is consistent with the P-ACT-LB data.
• Figure 4: Constraints on the parameters $n$ and $\tilde{\alpha}$ of the T-model, derived from the P-ACT-LB data as given in Eq. \ref{['act:constraints']}. The blue region corresponds to parameter values for which the predicted scalar spectral index given by Eq. \ref{['tmodnseq1']} from the T-model is consistent with the P-ACT-LB data.
• Figure 5: Constraints on the parameters $p$ and $\tilde{\mu}$ of the hilltop inflation model, derived from the P-ACT-LB data as given in Eq. \ref{['act:constraints']}. The blue region corresponds to parameter values for which the predicted scalar spectral index given by Eq. \ref{['hilltop:ns']} from the hilltop inflation is consistent with the P-ACT-LB data.