Seeking Inflation Fossils in the Cosmic Microwave Background

TL;DR

This paper investigates how fossil fields during inflation could leave detectable imprints on the CMB, specifically through BiPoSHs, and discusses their distinguishability and detectability.

Contribution

It introduces a formalism to quantify fossil field effects on CMB temperature fluctuations using bipolar spherical harmonics and analyzes their distinguishability and detectability.

Findings

Vector and tensor fossils induce BiPoSHs distinguishable by parity.

Scalar fossils produce different BiPoSH signatures than vector or tensor fossils.

Detectability estimates for fossil signals are provided for various types of fossils.

Abstract

If during inflation the inflaton couples to a "fossil" field, some new scalar, vector, or tensor field, it typically induces a scalar-scalar-fossil bispectrum. Even if the fossil field leaves no direct physical trace after inflation, it gives rise to correlations between different Fourier modes of the curvature or, equivalently, a nonzero curvature trispectrum, but without a curvature bispectrum. Here we quantify the effects of a fossil field on the cosmic microwave background (CMB) temperature fluctuations in terms of bipolar spherical harmonics (BiPoSHs). The effects of vector and tensor fossils can be distinguished geometrically from those of scalars through the parity of the BiPoSHs they induce. However, the two-dimensional nature of the CMB sky does not allow vectors to be distinguished geometrically from tensors. We estimate the detectability of a signal in terms of the scalar-scalar-fossil coupling for scalar, vector, and tensor fossils, assuming a local-type coupling. We comment on a divergence that arises in the quadrupolar BiPoSH from the scalar-scalar-tensor correlation in single-field slow-roll inflation.