Non-Gaussian Spikes from Chaotic Billiards in Inflation Preheating

TL;DR

This work performs highly accurate lattice simulations of supersymmetry-inspired quartic inflaton and coupling potentials in a separate-universe approximation to compute N(chi(i)) as a function of the (nearly homogeneous) initial condition chi(i).

Abstract

A new class of non-Gaussian curvature fluctuations ζ_{pr} (\bx) \equiv δN(χ_i) arises from the post-inflation preheating behaviour of a non-inflaton field χ_i. Its billiard-like chaotic dynamics imprints regular log-spaced narrow spikes in the number of preheating e-folds N(χ_i). We perform highly accurate lattice simulations of SUSY-inspired quartic inflaton and coupling potentials in a separate-universe approximation to compute N(χ_i) as a function of the (nearly homogeneous) initial condition χ_i. The super-horizon modes of χ_i(\bx) result in positive spiky excursions in ζ_{pr} and hence negative gravitational potential fluctuations added to the usual sign-independent inflaton-induced perturbations, observably manifested in large cosmic structures and as (polarized) temperature CMB cold spots.

Figures (3)

• Figure 1: The structure of $\delta N(\chi_i)$ on uniform Hubble hypersurfaces probed with $\sim 10^4$ lattice simulations from the end-of-inflation through the end-of-preheating for varying homogeneous $\chi_i$ initial conditions, for $g^2/\lambda = 2$. The periods $n \mu_0 T$ in $\ln \chi_i$ are marked by the large green circles, and the higher harmonics (revealed by the Fourier analysis) by smaller green circles. These locate the spikes in $\delta N(\chi_i)$. The effective field ${\langle F_{\text{NL}}\vert \chi_b+\chi_{>h} \rangle}$ marginalized over high spatial frequencies with $\sigma_{\text{HF}}$=$7\times 10^{-7}M_P$ (vertical line) yields the solid curve. A quadratic fit, $f_{\chi}( \chi_b+\chi_{>h})^2$, is also shown. An issue for our Hubble patch is whether the ultra-large scale $\chi_{>h}$ is large enough that the large scale structure fluctuations about it, $\pm \sigma_{b<h}$, encompass smoothed peaks in field space, or not. A typical value for $\sigma_{b<h}$ is $\sim 3\times 10^{-7}M_P$.
• Figure 2: Billiard trajectories of the $k=0$ modes $\phi(t)$ and $\chi(t)$ within the $\lambda \phi^4/4+g^2\chi^2\phi^2/2$ potential well. Upper panel has a "no-spike" initial value $\chi_i=3.6 \times 10^{-7} M_P$, and the bottom panel has a "spike" $\chi_i=3.9 \times 10^{-7} M_P$. The solid curves are the (fuzzy) potential wall without the inclusion of mass terms induced by field nonlinearities; the pale green and brighter green border areas include the induced masses at the instances $t=10.8T$ and asymptotically. Thin and thick parts of the trajectories denote before after $t=9.7T$, and up to $11.8T$, with the circle on it at $t=10.8T$. The inserts in the left upper corners of the panels show the first several periods of linear oscillations.
• Figure 3: Realizations of the nG map ${\langle F_{\text{NL}} \vert \chi_b \rangle}$ on the CMB sky. Top left shows a scale-invariant Gaussian random field realization $\chi_b (d_{\gamma dec} \hat{q} )$ in direction $\hat{q}$ on a sphere at the comoving distance to photon decoupling, $d_{\gamma dec}$ Top right shows the action of ${\langle F_{\text{NL}} \vert \chi_b \rangle}$ on it, using our Gaussian-line-profile approximation with 2 peaks at $\chi_p=\pm \nu_p \sigma_b$, for $\nu_p =3.5$. Middle left shows the map convolved with a CMB transfer function, and smoothed on a $1^\circ$ scale, right with $\nu_p =4.5$; both show "cold spot" intermittency.