Cosmological Fluctuations from Infra-Red Cascading During Inflation

TL;DR

This paper introduces a novel IR cascading mechanism during inflation, whereby a brief burst of χ-particle production in a model with ${\rm L}_{\rm int}= -\frac{g^2}{2}(\phi-\phi_0)^2 χ^2$ seeds non-equilibrium inflaton fluctuations that cascade power into IR modes. The authors combine lattice simulations and analytical calculations to show that IR cascading can produce a prominent bump in the curvature power spectrum, potentially dominating standard fluctuations for ${g^2>0.06}$, and that these fluctuations are highly non-Gaussian. A sequence of such bursts can generate broad-band non-Gaussian curvature fluctuations, with possible implications for trapped inflation and small-scale cosmology. The work highlights a non-thermal QFT effect during inflation that could imprint observable features in the CMB and large-scale structure, demanding careful consideration of back-reaction, renormalization, and non-Gaussianity.

Abstract

We propose a qualitatively new mechanism for generating cosmological fluctuations from inflation. The non-equilibrium excitation of interacting scalar fields often evolves into infra-red (IR) and ultra-violet (UV) cascading, resulting in an intermediate scaling regime. We observe elements of this phenomenon in a simple model with inflaton φand iso-inflaton χfields interacting during inflation via the coupling g^2 (φ-φ_0)^2 χ^2. Iso-inflaton particles are created during inflation when they become instantaneously massless at φ=φ_0, with occupation numbers not exceeding unity. We point out that very quickly the produced χparticles become heavy and their multiple re-scatterings off the homogeneous condensate φ(t) generates bremschtrahlung radiation of light inflaton IR fluctuations with high occupation numbers. The subsequent evolution of these IR fluctuations is qualitatively similar to that of the usual inflationary fluctuations, but their initial amplitude is different. The IR cascading generates a bump-shaped contribution to the cosmological curvature fluctuations, which can even dominate over the usual fluctuations for g^2>0.06. The IR cascading curvature fluctuations are significantly non-gaussian and the strength and location of the bump are model-dependent, through g^2 and φ_0. The effect from IR cascading fluctuations is significantly larger than that from the momentary slowing-down of φ(t). With a sequence of such bursts of particle production, the superposition of the bumps can lead to a new broad band non-gaussian component of cosmological fluctuations added to the usual fluctuations. Such a sequence of particle creation events can, but need not, lead to trapped inflation.

Figures (8)

• Figure 1: $|\dot\phi|/(M_pm)$ plotted against $m t$ for $g^2=0.1$ (where $m=V_{,\phi\phi}$ is the effective inflaton mass). Time $t=0$ corresponds to the moment when $\phi=\phi_0$ and $\chi$-particles are produced copiously. The solid red line is the lattice field theory result taking into account the full dynamics of re-scattering and IR cascading while the dashed blue line is the result of a mean field theory treatment which ignores re-scattering S. The dot-dashed black line is the inflationary trajectory in the absence of particle creation.
• Figure 2: Re-scattering diagram.
• Figure 3: The power spectrum of inflaton modes induced by re-scattering (normalized to the usual vacuum fluctuations) as a function of $\ln(k/k_\star)$, plotted for three representative time steps in the evolution, showing the cascading of power into the IR. For each time step we plot the analytical result (the solid line) and the data points obtained using lattice field theory simulations (diamonds). The time steps correspond to the following values of the scale factor: $a = 1.03, 1.04, 2.20$ (where $a = 1$ at the moment when $\phi = \phi_0$). By this time the amplitude of fluctuations is saturated due to the expansion of the universe. The vertical lines show the range of scales from our lattice simulation.
• Figure 4: Physical occupation number $n_k$ as a function of $\ln(k / k_\star)$ for $g^2=0.1$. The three curves correspond to the same series of time steps used in Fig. \ref{['Fig:pwr']}, and demonstrate the growing number of long wavelength inflaton modes which are produced as a result of IR cascading. Because the same $\chi$-particle can undergo many re-scatterings off the background condensate $\phi(t)$, the $\delta\phi$ occupation number is larger than the initial $\chi$ particle number (for $g^2=0.1$ one can achieve $n_\phi(k) \sim 30$ even though initially $n_\chi(k) \leq 1$). When $g^2 = 0.06$ the IR $\delta \phi$ occupation number exceeds unity within a single e-folding. The yellow envelope line shows the early onset of scaling behaviour associated with the scaling turbulent regime.
• Figure 5: The dependence of the power spectrum $P_\phi$ on the coupling $g^2$. The three curves correspond to $P_\phi$ for $g^2=0.01,0.1,1$, evaluated at a fixed value of the scale factor, $a = 2.20$. We see that even for small values of $g^2$ the inflaton modes induced by re-scattering constitute a significant fraction of the usual vacuum fluctuations after only a single e-folding.