Cosmological constraints from $\mu E$ cross-correlations

Understand

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.