Weak Gravity Conjecture in the sky: gravitational waves from preheating in Einstein-Maxwell-Scalar EFT

TL;DR

The paper develops an Einstein-Maxwell-Scalar EFT for reheating after inflation, focusing on inflaton decay to photons via a dimension-5 operator and graviton bremsstrahlung mediated by a R F F type coupling. By computing the differential graviton emission rate and evolving the produced gravitons with a Boltzmann equation, it connects the resulting high frequency GW spectrum to EFT scales and the CMB bound on dark radiation. The authors show that the GW signal can be strong enough to constrain the UV cutoff, yielding a lower bound of about 10^15 GeV for large-field inflaton masses when the coupling saturates the unitarity bound, while a Weak Gravity Conjecture bound weakens the signal and loosens the constraints. These results highlight high-frequency GWs as a potential cosmological probe of the UV completion of gravity and the consistency structure of EFTs in the early universe, motivating further EFT bootstrap studies and extensions to other gauge fields.

Abstract

The effective field theory (EFT) concept provides a necessary tool for obtaining general predictions of low-energy theory valid below its unitarity-breaking scale (cutoff scale). Early Universe inflation and subsequent reheating could be a unique setup for testing potentially observable effects coming from the derivative expansion of the corresponding EFT around the flat space vacuum. In this work, we consider an EFT describing perturbative reheating dominated by the decay of inflaton to photons caused by the dimension-5 operator $φF_{μν} F^{μν}$. We compute the graviton production during reheating and high frequency gravitational wave signal due to the bremsstrahlung effect in the presence of $R_{μνλρ}F^{μν} F^{λρ}$ operator. It may lead to the dominant contribution at high momenta if the EFT cutoff is lower than the Planck mass. Assuming the general consequences of the unitarity and causality constraints, which imply that all EFT operators should be present, and be suppressed by the scales following from the dimension analysis, we obtain the observational constraints (CMB bound for the dark radiation) on the mass of the inflaton and UV cutoff of gravity. We find that for the typical parameters of large field inflation models, the gravitational cutoff scale cannot be lower than $10^{15}$ GeV.

Figures (6)

• Figure 1: Feynman diagram of inflaton decays to two photons at the leading order. Here $\phi$ is the inflaton, and $\gamma$ stands for a photon. The variables $q$ and $p_1, p_2$ are the momenta of the inflaton and photons, respectively.
• Figure 2: Feynman diagrams of photon bremsstrahlung and inflaton decay at the leading order. Here $\phi$ is an inflaton, $\gamma$ is a photon, $h$ is a graviton, and $p,q,p_1,p_2$ are momenta of the corresponding particles. The matrix element of panel (a) vanishes due to transverse and traceless condition for the graviton polarization tensor.
• Figure 3: Integration limits on $z$. Here we set $\alpha=\beta=1$, $H_{inf}=10^{12}$ GeV, $g_{reh}=106.75$, $\Lambda_1=\Lambda_{UV}$, $\Lambda_2=\Lambda_{UV}^3/M_P^2$, $\Lambda_{UV}=10^{16.5}$ GeV, $m=10^{13}$ GeV.
• Figure 4: Examples of high frequency gravitational wave signal for the reheating scenarios determined by the choice $\Lambda_1=\Lambda_{UV}$, $\Lambda_2=\Lambda_{UV}^3/M_P^2$. The red and purple lines show the current CMB bound Planck:2018vyg on the number of relativistic degrees of freedom and the bound that can be potentially obtained in future observations, respectively.
• Figure 5: The dependence of the GW signal on the parametric choice of the scale $\Lambda_2$.