Nongaussian Isocurvature Perturbations from Inflation

TL;DR

This work shows that a simple two-field inflationary framework, where a secondary field σ acquires an effective mass of order the Hubble scale during inflation, can produce blue, non-Gaussian perturbations that are either isocurvature or adiabatic. Using the toy potential V(φ,σ) = $\tfrac{1}{2}M^2\phi^2 + \tfrac{1}{2}m^2\sigma^2 + \tfrac{1}{2}g^2\phi^2\sigma^2$ with m^2(H) = m^2 + α H^2, the authors show σ fluctuations lead to a density-perturbation spectrum |δ_k^ρ| ∝ (k/H)^{2α/3} and a spectral index n ≈ 1 + 4α/3 (e.g., α ≈ 0.45 gives n ≈ 1.6). This mechanism yields non-Gaussian perturbations whose character (isothermal vs. adiabatic) depends on the post-inflationary evolution of σ, offering a simple route to blue, non-Gaussian perturbations that can influence structure formation and CMB anisotropies.

Abstract

We present a class of very simple inflationary models of two scalar fields which leads to nongaussian isothermal perturbations with "blue" spectrum, n > 1. One of the models is inspired by supersymmetric theories where light scalar fields naturally acquire masses of the order of the Hubble constant H during inflation. Another model presumes that one of the fields has a nonminimal interaction with gravity. By a slight modification of parameters of these models one can obtain either gaussian isothermal perturbations, or nongaussian adiabatic perturbations with n > 1.