# CMB Spectral Distortion Constraints on Thermal Inflation

## TL;DR

This paper investigates how thermal inflation affects cosmic microwave background spectral distortions, showing that future measurements can constrain the inflationary scenario by detecting suppressed or standard levels of $ ext{-distortion}$.

## Contribution

It provides the first detailed calculation of CMB spectral distortions in thermal inflation models, linking distortion amplitude to inflationary parameters.

## Key findings

- Large suppression of $ ext{-distortion}$ for certain scales.
- Future experiments can constrain thermal inflation parameters.
- Predicted $ ext{-distortion}$ below standard value for specific scenarios.

## Abstract

Thermal inflation is a second epoch of exponential expansion at typical energy scales $V^{1/4} \sim 10^{6 \sim 8} \mathrm{GeV}$. If the usual primordial inflation is followed by thermal inflation, the primordial power spectrum is only modestly redshifted on large scales, but strongly suppressed on scales smaller than the horizon size at the beginning of thermal inflation, $k > k_{\rm b} = a_{\rm b} H_{\rm b}$. We calculate the spectral distortion of the cosmic microwave background generated by the dissipation of acoustic waves in this context. For $k_{\rm b} \ll 10^3 \mathrm{Mpc}^{-1}$, thermal inflation results in a large suppression of the $\mu$-distortion amplitude, predicting that it falls well below the standard value of $\mu \simeq 2\times 10^{-8}$. Thus, future spectral distortion experiments, similar to PIXIE, can place new limits on the thermal inflation scenario, constraining $k_{\rm b} \gtrsim 10^3 \mathrm{Mpc}^{-1}$ if $\mu \simeq 2\times 10^{-8}$ were found.