Signatures of Initial State Modifications on Bispectrum Statistics

TL;DR

The paper investigates how deviations from the Bunch-Davies vacuum during inflation imprint on the primordial bispectrum and its CMB projection. It shows that in canonical slow-roll inflation the strongest enfolded-type signal sits in collinear triangle configurations, yet standard local and equilateral templates largely miss this feature, limiting current constraints on initial-state modifications. Introducing a dimension-8 higher-derivative term can yield large, oscillatory bispectrum contributions that remain poorly matched to existing templates, underscoring the need for specialized templates. The study also demonstrates that 2D CMB projections may provide competitive constraints on the Bogoliubov parameter with appropriately tailored estimators, highlighting the potential gains from developing enfolded and oscillatory templates for future data.

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.