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Non-Gaussianity from Broken Symmetries

Edward W. Kolb, Antonio Riotto, Alberto Vallinotto

TL;DR

The paper investigates non-Gaussianity arising from broken global symmetries in the inflaton sector, showing that curvature perturbations can be generated during the decay (preheating) phase via isocurvature-to-adiabatic conversion. It develops an analytic treatment for a broken U(1) symmetry in an instant preheating setup, deriving a general formula for the nonlinearity parameter $f_{NL}$ and demonstrating that it can reach values as large as $\mathcal{O}(10^2)$, inversely tied to the symmetry-breaking parameter $x$. A broader result is presented: a universal expression for $f_{NL}$ in multi-field, symmetry-broken decays, with discussion of observational constraints and when large non-Gaussianity can arise. The work highlights non-Gaussianity as a powerful discriminator among inflationary mechanisms and suggests extending the analysis to include gravitational nonlinearities, which could induce momentum-dependent $f_{NL}$ signatures in future data.

Abstract

Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, $f_{NL}$, can be as large as 10^2.

Non-Gaussianity from Broken Symmetries

TL;DR

The paper investigates non-Gaussianity arising from broken global symmetries in the inflaton sector, showing that curvature perturbations can be generated during the decay (preheating) phase via isocurvature-to-adiabatic conversion. It develops an analytic treatment for a broken U(1) symmetry in an instant preheating setup, deriving a general formula for the nonlinearity parameter and demonstrating that it can reach values as large as , inversely tied to the symmetry-breaking parameter . A broader result is presented: a universal expression for in multi-field, symmetry-broken decays, with discussion of observational constraints and when large non-Gaussianity can arise. The work highlights non-Gaussianity as a powerful discriminator among inflationary mechanisms and suggests extending the analysis to include gravitational nonlinearities, which could induce momentum-dependent signatures in future data.

Abstract

Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, , can be as large as 10^2.

Paper Structure

This paper contains 7 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Model Overview
  3. An Analytic Example: The Broken U(1) Case in the Instant Preheating Scenario
  4. The Choice of the Background Field Landscape
  5. The Choice of the Inflaton Decay Process
  6. The Calculation of the Non-Linearity Parameter
  7. General Result for $f_{NL}$ and Conclusions

Figures (1)

  • Figure 1: Value of $f_{NL}$ for values of the symmetry breaking parameter of $x=10^{-1}$ (solid curve) and $x=10^{-2}$ (dashed curve). It seems important to stress that only a very small interval in the initial conditions $\theta_0$ will yield insignificant non-Gaussianity.