Inflationary Particle Production and the Swampland

TL;DR

This work analyzes inflation with an infinite tower of states whose masses decrease exponentially along the inflaton direction, motivated by the Swampland Distance Conjecture. By deriving backreaction and perturbation effects, it shows that corrections to observables scale as $\left(H/\Lambda_{\text{sp}}\right)^{2+p}$ with $p\ge1$, ensuring negligible impact on inflationary predictions as long as the EFT remains weakly coupled ($H\ll\Lambda_{\text{sp}}$). Across several well-motivated potentials, the tower contributions to $n_s$, $r$, and $f_{\mathrm{NL}}$ remain small, with inverse hilltop potentials offering the best compatibility with current data when towers are present. The results imply that UV completions predicting towers do not destabilize standard single-field inflationary phenomenology unless one approaches the quantum gravity cutoff, providing robustness to inflationary predictions within the Swampland-inspired framework.

Abstract

We investigate the impact of particle production during inflation in scenarios where an infinite tower of states features a mass scale that decreases exponentially along the inflationary trajectory. Such couplings naturally arise in string effective field theories and are in fact motivated by the Swampland Distance Conjecture (SDC). We show that the corrections to inflationary observables sourced by the tower scale as $(H/Λ_{\text{sp}})^{2+p}$, with $H$ being the Hubble scale, $Λ_{\text{sp}}$ being the species scale, that is the quantum gravity cut-off, and $p\geq 1$ characterizes the density of states in the tower. As a result, in gravitationally weakly coupled cosmological effective theories, the tower-induced contributions are suppressed relative to the standard single-field predictions, leaving the inflationary phenomenology essentially unchanged. We demonstrate this explicitly across a set of well-motivated inflationary potentials, and we compare the resulting predictions with the most recent observational constraints, including those from the Atacama Cosmology Telescope.

Figures (4)

• Figure 1: Exponentially decaying tower $m_{\text{t}}$ and species $\Lambda_{\text{sp}}$ scales compared to the Hubble scale. There is an intermediate regime in the field excursion of the inflaton in which the inflationary EFT must include the effects of the light tower of species.
• Figure 2: Two-point correlation function for the $\chi$ fields, compared to the expected value of vacuum modes (solid blue line). The solid red line denotes the approximate solution of \ref{['eq:xi_eq_2']} (divided by the scale factor) for $k|\tau|\ll\sqrt{2-\delta_n}$, while the dashed black line is the numerical solution. Here we have fixed $\delta_n=0.01$, $\gamma=0.25$, $|\dot{\varphi}|/H=1/\sqrt{120}$, corresponding to the single-field solution of chaotic inflation with a linear potential.
• Figure 3: Region allowed by the constraints imposed by the conditions reported in \ref{['tab:constraints']} (red dotted lines) for the parameter space of our model, in terms of the species coupling $\gamma$ vs the ratio between IR and UV scales $H/\Lambda_{\text{sp}}$. We show the regions for several example potentials considered in this work. The allowed regions are represented by shaded grey areas, with purple bands highlighting the values of $\gamma$ compatible with the SDC.
• Figure 4: Theoretical predictions for $n_s$ vs $r$ all potentials considered in this work (see main legend) compared with observational constraints represented by colorful shaded areas (see top left legend and main text for the different data combinations). We stress that any meaningful deviations from single-field inflation predictions (corresponding to $H/\Lambda_{\text{sp}}\simeq 0$ and represented with black dots) only occur near $H/\Lambda_{sp}\simeq$ 1 where the EFT description is expected to break down. To not saturate this bound, the maximal value we employ in this plot is $\Lambda_{\text{sp}}\leq 0.5$, where all colorful lines end in either upward ($\blacktriangle$) or downward ($\blacktriangledown$) colorful triangles, representing $\gamma =\sqrt{1/2}$ and $\gamma =\sqrt{3/2}$, respectively.