Cosmological constraints from $\mu E$ cross-correlations

TL;DR

This paper derives formulas for cross correlations between cosmic microwave background spectral $\u03bc$ distortions and linear perturbations, providing new tests for primordial non-Gaussianity and assessing their detectability with future experiments.

Contribution

It presents general expressions for $\u03bc$-perturbation cross correlations applicable to scalar and tensor modes, and evaluates their potential detectability.

Findings

Cross correlations can test squeezed primordial non-Gaussianity.

Signal-to-noise ratios suggest detectability with future experiments like PIXIE.

Scale-dependent nonlinearity parameters can be constrained at 1$ extsigma$ level.

Abstract

We derive general expressions of the $C^{\mu X}_l$, the cross correlation function between the cosmic microwave background spectral $\mu$ distortion and the linear perturbations in the cosmic microwave background such as the temperature perturbations and the polarizations. The cross correlations are known as new tests for the extremely squeezed shape of primordial non-Gaussianity, which is inaccessible through the direct observations of the temperature 3-point functions. Our formulae are applicable to the arbitrary combinations of the scalar and the tensor perturbations, and we discuss the potential for detecting these quantities. We provide signal-to-noise ratio of the $\mu E$ as well as $\mu T$, based on an experiment like the Primordial Inflation Explorer. We also find the signal-to-noise ratio from the scale dependent nonlinearity. For instance, we show that $f^{\rm loc}_{\rm NL}(k_1,k_2,k_3)=\left(k_1k_2k_3\right)^{1/3}k_0^{-1}F_0$ with $k_0=0.05{\rm Mpc}^{-1}$ can be detectable at 1$\sigma$ level even for $F_0 \sim \mathcal O(1)$.