Preheating After Modular Inflation

TL;DR

This work analyzes reheating after modular (Kähler moduli/Roulette) inflation within large-volume string compactifications. It demonstrates that preheating is dominated by explosive, nonperturbative production of inflaton fluctuations due to a highly nonlinear potential, featuring simultaneous tachyonic instability and broad-band parametric resonance. It then details three main reheating pathways—(i) direct D7-brane couplings on the inflationary cycle, (ii) indirect decay when the SM sits on a non-inflationary cycle, and (iii) a stringy route as the inflationary cycle approaches the string scale—providing decay rates and reheating temperatures ${T_r}$ that are sensitive to the overall volume $oldsymbol{\mathcal{V}}$ and subject to decompactification and gravitino constraints. The results underscore the UV-complete, highly model-dependent nature of reheating in string cosmology and hint at distinctive phenomenology tied to the chosen SM embedding and the possible stringy degrees of freedom active during reheating.

Abstract

We study (p)reheating in modular (closed string) inflationary scenarios, with a special emphasis on Kahler moduli/Roulette models. It is usually assumed that reheating in such models occurs through perturbative decays. However, we find that there are very strong non-perturbative preheating decay channels related to the particular shape of the inflaton potential (which is highly nonlinear and has a very steep minimum). Preheating after modular inflation, proceeding through a combination of tachyonic instability and broad-band parametric resonance, is perhaps the most violent example of preheating after inflation known in the literature. Further, we consider the subsequent transfer of energy to the standard model sector in scenarios where the standard model particles are confined to a D7-brane wrapping the inflationary blow-up cycle of the compactification manifold or, more interestingly, a non-inflationary blow up cycle. We explicitly identify the decay channels of the inflaton in these two scenarios. We also consider the case where the inflationary cycle shrinks to the string scale at the end of inflation; here a field theoretical treatment of reheating is insufficient and one must turn instead to a stringy description. We estimate the decay rate of the inflaton and the reheat temperature for various scenarios.

Figures (3)

• Figure 1: The left panel shows the effective potential for the canonical Kähler modulus $\phi$ along the axion trough, $U(\phi,(2l+1)\pi / a_2)$ showing the long exponentially flat region relevant for inflation and also the steep minimum relevant for the preheating phase of post-inflationary oscillations. We have labeled the point where inflation ends (where the $\epsilon$ slow roll parameter is unity) and also the point where the effective mass-squared $V"(\phi)$ flips sign, corresponding to the cross-over between the tachyonic and non-tachyonic regions. The right panel shows the oscillatory time evolution of the homogeneous inflaton $\phi_0(t)$ at the end of inflation.
• Figure 2: The behaviour of linear Kähler fluctuations during preheating after modular inflation illustrating the combination of tachyonic instability and parametric resonance. The left panel shows the mode behaviour for $k = 0.01 m_\phi$ (corresponding to the IR tachyonic regime) while the right panel shows the mode behaviour for $k = 0.5 m_\phi$ (corresponding to the UV regime of parametric resonance). The middle panel is $k = 0.08 m_\phi$, corresponding to the intermediate regime where both effects are active.
• Figure 3: The left panel shows the time dependence of the effective photon mass, $M_{\gamma,\mathrm{eff}}^2(t)$. The right panel shows the Floquet exponent $\mu_k$ for the mode functions $A_k(t) \sim e^{\mu_k t / T}$.