The $R^2$-Higgs inflation: $R^3$ contribution and preheating after ACT and SPT data

TL;DR

This work investigates whether the high scalar spectral index $n_s$ reported by ACT/SPT+DESI can be reconciled with $R^2$-Higgs inflation by adding a dimension-six curvature term $R^3$ in the action. Using a doubly covariant two-field formalism, the authors derive the full background and linear perturbation equations beyond slow-roll and show that the $R^3$ term can tilt the inflationary dynamics to match the observed $n_s$ and amplitude, while the preheating epoch plays a crucial role in matching the CMB scale to the inflationary horizon. They find that Higgs-field preheating, with a nonminimal coupling $\xi_H$ of order $10$, can drive rapid reheating; for one benchmark point preheating via Higgs quanta yields $T_{\rm pre} \sim 5\times 10^{14}$ GeV and $\mathcal{N}_{\rm pre} \approx 1.8$, bringing the scale matching very close to the data. The study highlights both the potential of the $R^3$ modification to explain the data and the sensitivity to post-inflationary dynamics, noting that decays, backreaction, and gauge preheating require further analysis.

Abstract

The $R^2$-Higgs inflation is one of the simplest yet best-fit models consistent with Planck data. The higher spectral index $n_s$ recently reported by the combined cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT), South Pole Telescope (SPT), and Planck, along with baryonic acoustic oscillation data from the Dark Energy Spectroscopic Instrument (DESI), disfavors the single-field-like regime of $R^2$-Higgs inflation at approximately $2σ$. Following a doubly covariant formalism, we show that the $R^2$-Higgs inflation, when modified by a dimension-six $R^3$ term, can account for the high $n_s$ reported by CMB+BAO. In this regard, we find that preheating may play a pivotal role. We also show that if the nonminimal coupling between the Ricci scalar $R$ and the Higgs field is $\mathcal{O}(10)$, then preheating via the production of Higgs quanta may help explain the reported observations.

Figures (7)

• Figure 1: The effective potential $W_{\rm{eff}}(\phi)$ vs $\phi$ plots for ($\xi_H = 1$, $\xi_R = 2\times 10^9$), ($\xi_H = 10$, $\xi_R = 2.3\times 10^9$) and ($\xi_H = 100$, $\xi_R = 2.5\times 10^9$) for different values of $\xi_c$.
• Figure 2: The evolution of $\varphi$, $h_0$ and $H$ with respect to cosmological time $t$ for BP$a$.
• Figure 3: The $\mathcal{P}_{\mathcal{R}}(k)$ and $n_s$ vs $k$ for both the BPs. Here the $n_s$ is evaluated directly utilizing Eq. \ref{['specin1']} and $\mathcal{P}_{\mathcal{R}}(k)$ via Eq. \ref{['eq:powadia']}.
• Figure 4: The evolution of $\mathcal{P}_{\mathcal{R}}(k_*)$ and $\mathcal{P}_{\mathcal{S}}(k_*)$ after horizon exit for both the BPs.
• Figure 5: The evolution of $m_{\mathrm{eff},(I)}^2(\tau)$ as function of $\mathcal{N}$. See text for details.