Nonminimal infrared gravitational reheating in light of ACT observation

TL;DR

This work proposes a non-minimal infrared gravitational reheating mechanism in which a scalar χ non-minimally coupled to gravity, with ξ χ^2 R, experiences tachyonic growth of infrared modes that reheat the universe as they reenter the horizon. The authors compare this non-perturbative infrared production to conventional perturbative Boltzmann reheating in both Jordan and Einstein frames, and embed the scenario within the α-attractor E-model, deriving reheating parameters and observational constraints. By combining r_{0.05} bounds, isocurvature limits, and ΔN_eff, they identify a narrow allowed ξ range for various w_φ that yields successful reheating, with the parameter space favoring w_φ ≳ 0.6 and ξ ≈ 2.1–2.95; this region also predicts strong secondary gravitational waves detectable by future detectors like LISA, BBO, DECIGO, and ET. The results indicate that infrared gravitational reheating can dominate over traditional sub-Hubble production in precise regimes, offering testable predictions and tightening the viability of α-attractor models in light of ACT/DESI data.

Abstract

Inflation is known to produce large infrared scalar fluctuations. Further, if a scalar field $(χ)$ is non-minimally coupled with gravity through $ξχ^2 R$, those infrared modes experience \textit{tachyonic instability} during and after inflation. Those large non-perturbative infrared modes can collectively produce hot Big Bang universe upon their horizon entry during the post-inflationary period. We indeed find that for reheating equation of state (EoS), $w_φ > 1/3$, and coupling strength, $ξ>1/6$, large infrared fluctuations lead to successful reheating. We further analyze perturbative reheating by solving the standard Boltzmann equation in both Jordan and Einstein frames, and compare the results with the non-perturbative ones. Finally, embedding this infrared reheating scenario into the well-known $α-$attractor inflationary model, we examine possible constraints on the model parameters in light of the latest ACT, DESI results. To arrive at the constraints, we take into account the latest bounds on tensor-to-scalar ratio, $r_{0.05}\leq 0.038$, isocurvature power spectrum, $\mathcal{P}_{\mathcal{S}} \lesssim 8.3\times 10^{-11}$, and effective number of relativistic degrees of freedom, $ΔN_{\rm eff} \lesssim 0.17 $. Subject to these constraints, we find successful reheating to occur only for EoS $w_φ\gtrsim 0.6$, which translates to a sub-class of $α-$attractor models being favored and placing them within the 2$σ$ region in the $ n_s-r$ plane of the latest ACT, DESI data. In this range of EoS, we find that the coupling strength should lie within $2.11\lesssimξ\lesssim 2.95$ for $w_φ=0.6$. Finally, we compute secondary gravitational wave signals induced by the scalar infrared modes, which are found to be strong enough to be detected by future GW observatories, namely BBO, DECIGO, LISA, and ET.

Figures (9)

• Figure 1: Figure represents the measure of adiabaticity violation in terms of parameter $|(d\omega_k/d(\eta k_{\rm end})/\omega_k^2|$ with $\eta k_{\rm end}$ for different coupling strengths $\xi$ (left panel) and different scales $k/k_{\rm end}$ (right panel) for a specific EoS $w_{\phi}=1/2$. In both panels, the black dashed line indicates adiabaticity parameter, $|(d\omega_k/d(\eta k_{\rm end})/\omega_k^2|=1$. Any value of $|(d\omega_k/d(\eta k_{\rm end})/\omega_k^2|>1$ depicted by the gray shaded region indicates the violation of adiabaticity. In the left panel of this figure, for the given scale $k/k_{\rm end}=0.01$, with the increase of $\xi$ values, the peak of the adiabaticity parameter gradually shifts from the inflationary to the post-inflationary phase. This indicates that the super-horizon modes can still grow during reheating for higher coupling $\xi$. For $\xi=0$, the instability effect is only present in the inflationary phase. In the right panel, it shows that for a given non-minimal coupling $\xi$ with the increase of $k/k_{\rm end}$ (small scale), the modes tend to remain adiabatic through the evolution.
• Figure 2: Figure represents the variation of dimensionless field variable $|\chi_k|^2 \times k_{\rm end}$ with dimensionless time $\eta k_{\rm end}$ in the post-inflationary phase. The left panel of the figure shows that with the increase of $\xi$, the post-inflationary instability effect becomes vital for a particular super-Hubble mode at the inflation end. The super-horizon growth will sustain until a particular mode enters the horizon and after horizon entry, the field mode will be oscillatory. In the right panel of the figure, it is observed that the longer the wavelength, the stronger the instability growth for a particular coupling strength, and this is true for any non-minimal coupling strength $\xi$.
• Figure 3: Figure represents a comparison of $T_{\rm re}$ vs $\xi$ variation for different EoS between perturbative(Jordan frame) and non-perturbative analysis. Solid lines correspond to the non-perturbative or Bogoliubov predictions, and dashed lines correspond to the perturbative Boltzmann predictions in the Jordan frame. Red dots on each color line indicate the maximum value of the coupling strength, $\xi_{\rm max}$, corresponding to each EoS consistent with large-scale observational bounds ( gravitational wave and isocurvature), and the overlapping shaded region is ruled out by the latest CMB scale tensor-to-scalar ratio and isocurvature bounds for all four EoS. For a given EoS, any $\xi$, exceeding the red dot is disallowed by observation, and its associated $T_{\rm re}$ lies inside the shaded region. There are four demarcating lines inside the shaded region. From the top, the first one corresponds to $w_{\phi}=9/11$, the second one to $w_{\phi}=5/7$, the third one to $w_{\phi}=3/5$, and the fourth one to $w_{\phi}=1/2$.
• Figure 4: Left Panel: Figure represents constraints on $\xi$ for different post-inflationary EoS. The horizontal black dashed line indicates the maximum bound on $r$ at the CMB scale, $r_{0.05}=0.038$, and the vertical colored dashed lines show the maximum allowed value of the coupling $\xi_{\rm max}$ for different EoS subject to this bound. For a given EoS, $r_{0.05}$ for any $\xi>\xi_{\rm max}$(shaded region) is hence disallowed by the current bound. Right panel: Figure represents the constraints on $\xi$ from isocurvature power spectrum for different post-inflationary EoS. The horizontal black dashed line indicates the current bound on CMB scale isocurvature amplitude $\mathcal{P}_{\mathcal{S}}(k_{\ast})=8.3\times 10^{-11}$, and the vertical colored dashed lines show the maximum allowed value of $\xi$ for different EoS. For a given EoS, $\mathcal{P}_{\mathcal{S}}(k_{\ast})$ for any $\xi>\xi_{\rm max}$(shaded region) is hence disallowed by the current isocurvature bound.
• Figure 5: Figure represents the total gravitational wave spectra (PGW+SGW) for today with the variation of non-minimal coupling strength for different reheating EoS in the non-minimal coupling-induced infrared reheating background. For each EoS, a particular coupling $\xi$ exists at which primary strength starts to overcome the secondary one at all frequency regimes, and the total GW spectrum closely follows the primary behavior, as obvious in this figure. For instance, for $w_{\phi}=2/3,~ \xi\lesssim 2.5$, PGW strength starts to surpass the secondary strength in the entire frequency scale. In this plot, we have taken the lowest frequency, $f_{\ast}= \left(k_{\ast}/2\pi\right)\sim 7.75\times 10^{-17}$ Hz, and the highest frequency, $f_{\rm end}=\left(k_{\rm end}/2\pi\right)\sim 10^{11}$ Hz for all the EoS.