(P)reheating Effects of the K\"ahler Moduli Inflation I Model

Abstract

We investigate reheating in the string-theory-motivated K\"ahler Moduli Inflation I (KMII) potential, coupled to a light scalar field $\chi$ and produce constraints and forecasts based on Cosmic Microwave Background (CMB) and gravitational wave observables. We implement a Markov Chain Monte Carlo (MCMC) sampling method to compute the adopted model's parameter ranges allowed by the current CMB observations. Floquet analysis and numerical lattice simulations are performed to analyze the nonlinear effects of the model's (p)reheating phase. We derive bounds on the $\Lambda$CDM parameters $A_s$, $n_s$, $n_{\mathrm{run}}$, and $r$ based on \textit{Planck} results, finding that correlations between model parameters severely constrain the range of these parameters allowed within this model. While the KMII potential's non-vanishing minimum may provide a possible source for the observed dark energy density $\rho_{\mathrm{DE}}$ this cannot be tested with current observations. We estimate the $95\%$ CI bounds on the inflaton mass $m_{\phi}$ and reheating temperature $T_{\mathrm{reh}}$ to be $2.1 \times 10^{13} \, \mathrm{GeV} \lesssim m_{\phi} \lesssim 3.2 \times 10^{13} \, \mathrm{GeV}$ and $T_{\mathrm{reh}} \gtrsim 1.8 \times 10^{3} \, \mathrm{GeV}$, respectively. We observe {both} self-resonance and parametric resonance instability band structures in our Floquet analysis results. Finally, we do not observe any formation of oscillon configurations in our lattice simulations; however, our results predict a stochastic gravitational wave background generated during preheating that would be observable today in the $10^{9}$ - $10^{11} \, \mathrm{Hz}$ frequency range.