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Curvature perturbation from symmetry breaking the end of inflation

Laila Alabidi, David Lyth

TL;DR

The paper develops a two-field hybrid inflation model in which inflation ends on an ellipse-shaped surface that breaks $SO(2)$ symmetry, enabling the end-of-inflation contribution to the curvature perturbation $oldsymbol{ ablaoldsymbol{} ilde{ abla}}$. By applying the Lyth formalism, it derives the end-of-inflation contribution to $oldsymbol{ ablaoldsymbol{}}$ and shows how the spectrum and non-Gaussianity parameters ${f_{ m NL}}$ and ${\tau_{ m NL}}$ depend on the ellipse’s orientation and symmetry-breaking strength. It identifies regimes where the end perturbation dominates or is subdominant, and demonstrates that observable non-Gaussianity can arise for large symmetry breaking and favorable geometry, albeit with potential location-dependence concerns. The results provide a concrete route to generate detectable non-Gaussianity in a multi-field inflationary setup without introducing ad hoc extra fields, with implications for CMB and large-scale structure constraints.

Abstract

We consider a two-field hybrid inflation model, in which the curvature perturbation is predominantly generated at the end of inflation. By finely tuning the coupling of the fields to the waterfall we find that we can get a measurable amount of non-gaussianity.

Curvature perturbation from symmetry breaking the end of inflation

TL;DR

The paper develops a two-field hybrid inflation model in which inflation ends on an ellipse-shaped surface that breaks symmetry, enabling the end-of-inflation contribution to the curvature perturbation . By applying the Lyth formalism, it derives the end-of-inflation contribution to and shows how the spectrum and non-Gaussianity parameters and depend on the ellipse’s orientation and symmetry-breaking strength. It identifies regimes where the end perturbation dominates or is subdominant, and demonstrates that observable non-Gaussianity can arise for large symmetry breaking and favorable geometry, albeit with potential location-dependence concerns. The results provide a concrete route to generate detectable non-Gaussianity in a multi-field inflationary setup without introducing ad hoc extra fields, with implications for CMB and large-scale structure constraints.

Abstract

We consider a two-field hybrid inflation model, in which the curvature perturbation is predominantly generated at the end of inflation. By finely tuning the coupling of the fields to the waterfall we find that we can get a measurable amount of non-gaussianity.

Paper Structure

This paper contains 6 sections, 24 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. The Equations
  4. Parameter Constraints I
  5. Parameter Constraints II
  6. Discussion

Figures (4)

  • Figure 1: Single field inflation ends on a surface of constant energy density, we however are considering the case of multiple-fields driving inflation, and thus inflation ends on a surface of non-constant energy density, as represented by the dotted line. It is clear to see that $t_1$ and $t_2$ produce different amount of inflation, thus the family of trajectories is still curved at the end, and the curvature perturbation is increased by an amount $N_e=\delta{}N$.
  • Figure 2: Representation of the setup, where the surface at the end of inflation is an ellipse, therefore varying the trajectory (or the orientation of the ellipse) varies the amount of inflation. The dotted circles correspond to scenarios in which all trajectories are equal,as in single field inflation
  • Figure 3: Plot of $\frac{3}{5}f_{NL}$ vs. $h/g$ for three values of $g/f$. It is clear from the graph that we have a measurable (significant) non-gaussianity for $h\gg{}g$. The shaded region corresponds to the region which can be measured, and which has not yet been ruled out
  • Figure 4: $\frac{3}{5}f_{NL}$ versus the angle $\theta$ for various degrees of symmetry breaking the end of inflation. The bold lines correspond to the WMAP upper bound at $1\sigma$$n=0.953$ and the dotted lines corresponds to the $2\sigma$ upper bound $n=0.978$.