Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Trans-Planckian enhancements of the primordial non-Gaussianities

Hael Collins, R. Holman

TL;DR

This work investigates how short-distance Lorentz-violating effects during inflation can enhance primordial non-Gaussianities. Using an effective-field-theory framework with two leading cubic operators that break time vs. space symmetries, it computes the resulting three-point function amplitudes ${\cal A}_1$ and ${\cal A}_2$ and translates them into an effective $f_{\rm nl}$ with distinct momentum dependences. It finds that Case I yields a nearly scale-independent enhancement $f_{\rm nl} \sim \sqrt{\epsilon}\,{M_{\rm pl}\over M}$, while Case II produces a scale-dependent, oscillatory signal that grows with $k$, both subject to stringent current and future observational bounds. The results imply that three-point constraints can tightly bound the trans-Planckian scale $M$, often more strongly than the power spectrum, guiding the viability of Lorentz-violating scenarios in inflation.

Abstract

This article examines how breaking a Lorentz-invariant description of nature at tiny space-time intervals would affect the non-Gaussian character of the pattern of primordial perturbations left by inflation. We specifically study a set of irrelevant operators that preserve the spatial symmetries of the usual inflationary background. The non-Gaussian component in the primordial fluctuations can be much larger than the usual, small, inflationary prediction and can thus lead to much stronger constraints on the role of "trans-Planckian" physics in inflation than those from the measurements of the primordial power spectrum.

Trans-Planckian enhancements of the primordial non-Gaussianities

TL;DR

This work investigates how short-distance Lorentz-violating effects during inflation can enhance primordial non-Gaussianities. Using an effective-field-theory framework with two leading cubic operators that break time vs. space symmetries, it computes the resulting three-point function amplitudes and and translates them into an effective with distinct momentum dependences. It finds that Case I yields a nearly scale-independent enhancement , while Case II produces a scale-dependent, oscillatory signal that grows with , both subject to stringent current and future observational bounds. The results imply that three-point constraints can tightly bound the trans-Planckian scale , often more strongly than the power spectrum, guiding the viability of Lorentz-violating scenarios in inflation.

Abstract

This article examines how breaking a Lorentz-invariant description of nature at tiny space-time intervals would affect the non-Gaussian character of the pattern of primordial perturbations left by inflation. We specifically study a set of irrelevant operators that preserve the spatial symmetries of the usual inflationary background. The non-Gaussian component in the primordial fluctuations can be much larger than the usual, small, inflationary prediction and can thus lead to much stronger constraints on the role of "trans-Planckian" physics in inflation than those from the measurements of the primordial power spectrum.

Paper Structure

This paper contains 7 sections, 77 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The trans-Planckian problem reviewed
  3. Time-evolution
  4. The three-point function
  5. Case I: The operator $H^2\varphi^3$
  6. Case II: The operator $\varphi^2\vec{\nabla}\cdot\vec{\nabla}\varphi$
  7. Conclusions

Figures (1)

  • Figure 1: Two representative cases for the momenta appearing in the transform of the three-point function. In the figure on the left, all of the momenta have more or less the same magnitude, $k_1\approx k_2\approx k_3$, while the figure on the right shows the case where one of the momenta is much smaller than the other two, $k_1\approx k_2 \gg k_3$, for example.