Nonminimal infrared gravitational reheating in light of ACT observation

Abstract

Inflation is known to produce large infrared scalar fluctuations. Further, if a scalar field $(\chi)$ is non-minimally coupled with gravity through $\xi \chi^2 R$, 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), $w_{\phi} > 1/3$, and coupling strength, $\xi>1/6$, 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 $\alpha-$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, $\Delta N_{\rm eff} \lesssim 0.17 $. Subject to these constraints, we find successful reheating to occur only for EoS $w_{\phi}\gtrsim 0.6$, which translates to a sub-class of $\alpha-$attractor models being favored and placing them within the 2$\sigma$ 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 $2.11\lesssim\xi\lesssim 2.95$ for $w_{\phi}=0.6$. 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.