# Probing the Running of Primordial Bispectrum and Trispectrum using CMB Spectral Distortions

## TL;DR

This paper investigates how the running of primordial higher order correlation functions affects CMB spectral distortions, showing that it can significantly enhance signals and make them detectable with future experiments.

## Contribution

It demonstrates that the running of primordial bispectrum and trispectrum can greatly amplify CMB spectral distortion signals, enabling their potential detection.

## Key findings

- Running enhances spectral distortion signals by several orders of magnitude.
- Signal-to-noise ratios can reach up to 4000 for PIXIE-like experiments.
- CMB spectral distortions can serve as probes for the running of higher order correlation functions.

## Abstract

We compute the impact of the running of higher order density correlation functions on the two point functions of CMB spectral distortions (SD). We show that having some levels of running enhances all of the SDs by few orders of magnitude which might make them easier to detect. Taking a reasonable range for $ |n_{f_{NL}} |\lesssim 1.1$ and with $f_{NL} = 5$ we show that for PIXIE like experiment, the signal to noise ratio, $(S/N)_{i}$, enhances to $\lesssim 4000$ and $\lesssim 10$ for $\mu T$ and $yT$ toward the upper limit of $n_{f_{NL}}$. In addition, assuming $ |n_{\tau_{NL}}|< 1$ and $\tau_{NL} = 10^3$, $(S/N)_{i}$ increases to $\lesssim 8\times 10^{6}$, $\lesssim 10^4$ and $\lesssim 18$ for $\mu\mu$, $\mu y$ and $yy$, respectively. Therefore CMB spectral distortion can be a direct probe of running of higher order correlation functions in the near future.