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Enhanced Non-Gaussianity from Excited Initial States

R. Holman, Andrew J. Tolley

TL;DR

This work investigates how non-Bunch-Davies initial states influence inflationary non-Gaussianity, especially the bispectrum. It uses an effective field theory in an expanding FRW background and the in-in formalism to compute tree-level bispectra for both renormalizable and higher-derivative interactions, with initial states described by Bogoliubov coefficients and a Hadamard condition. It finds that initial excitations can enhance the bispectrum, particularly for flattened triangles, with the enhancement scaling roughly as $k_t/(a(eta_0) M)$ for certain operators; higher-derivative terms can yield large $f_{NL}$ up to about $10^4$ within backreaction and EFT bounds. These effects could be observable in current or future CMB data, providing a probe of the inflaton's initial state and of early-time physics, and they connect to transplankian considerations by highlighting how the initial state can leave a measurable imprint.

Abstract

We use the techniques of effective field theory in an expanding universe to examine the effect of choosing an excited inflationary initial state built over the Bunch-Davies state on the CMB bi-spectrum. We find that even for Hadamard states, there are unexpected enhancements in the bi-spectrum for certain configurations in momentum space due to interactions of modes in the early stages of inflation. These enhancements can be parametrically larger than the standard ones and are potentially observable in current and future data. These initial state effects have a characteristic signature in $l$-space which distinguishes them from the usual contributions, with the enhancement being most pronounced for configurations corresponding to flattened triangles for which two momenta are collinear.

Enhanced Non-Gaussianity from Excited Initial States

TL;DR

This work investigates how non-Bunch-Davies initial states influence inflationary non-Gaussianity, especially the bispectrum. It uses an effective field theory in an expanding FRW background and the in-in formalism to compute tree-level bispectra for both renormalizable and higher-derivative interactions, with initial states described by Bogoliubov coefficients and a Hadamard condition. It finds that initial excitations can enhance the bispectrum, particularly for flattened triangles, with the enhancement scaling roughly as for certain operators; higher-derivative terms can yield large up to about within backreaction and EFT bounds. These effects could be observable in current or future CMB data, providing a probe of the inflaton's initial state and of early-time physics, and they connect to transplankian considerations by highlighting how the initial state can leave a measurable imprint.

Abstract

We use the techniques of effective field theory in an expanding universe to examine the effect of choosing an excited inflationary initial state built over the Bunch-Davies state on the CMB bi-spectrum. We find that even for Hadamard states, there are unexpected enhancements in the bi-spectrum for certain configurations in momentum space due to interactions of modes in the early stages of inflation. These enhancements can be parametrically larger than the standard ones and are potentially observable in current and future data. These initial state effects have a characteristic signature in -space which distinguishes them from the usual contributions, with the enhancement being most pronounced for configurations corresponding to flattened triangles for which two momenta are collinear.

Paper Structure

This paper contains 1 section, 6 equations, 1 figure.

Table of Contents

  1. Introduction

Figures (1)

  • Figure 1: Momentum triangles which dominate the bi-spectrum: 1. Equilateral triangles arising from Hubble-horizon crossing. 2. Squeezed or local triangles arising from super-Hubble evolution. 3. Flattened triangles arising from intial state effects.