Signatures of Initial State Modifications on Bispectrum Statistics

TL;DR

This paper investigates how modifications to the initial state of the inflaton can affect the bispectrum of primordial curvature perturbations, revealing oscillatory signals that are difficult to detect with current templates but could provide new constraints on early universe models.

Contribution

It introduces the impact of higher derivative terms on the bispectrum, highlighting oscillatory features that challenge existing observational templates and suggesting new avenues for constraining initial state modifications.

Findings

Localized enhancements are insensitive to standard templates.

Higher derivative terms produce oscillatory bispectrum signals.

Oscillatory signals are nearly orthogonal to current observational templates.

Abstract

Modifications of the initial-state of the inflaton field can induce a departure from Gaussianity and leave a testable imprint on the higher order correlations of the CMB and large scale structures in the Universe. We focus on the bispectrum statistics of the primordial curvature perturbation and its projection on the CMB. For a canonical single-field action the three-point correlator enhancement is localized, maximizing in the collinear limit, corresponding to enfolded or squashed triangles in comoving momentum space. We show that the available local and equilateral template are very insensitive to this localized enhancement and do not generate noteworthy constraints on initial-state modifications. On the other hand, when considering the addition of a dimension 8 higher order derivative term, we find a dominant rapidly oscillating contribution, which had previously been overlooked and whose significantly enhanced amplitude is independent of the triangle under consideration. Nevertheless, the oscillatory nature of (the sign of) the correlation function implies the signal is nearly orthogonal to currently available observational templates, strongly reducing the sensitivity to the enhancement. Constraints on departures from the standard Bunch-Davies vacuum state can be derived, but also depend on the next-to-leading terms. We emphasize that the construction and application of especially adapted templates could lead to CMB bispectrum constraints on modified initial states already competing with those derived from the power spectrum.