Probing early-universe phase transitions with CMB spectral distortions

Global, symmetry-breaking phase transitions in the early universe can generate scaling seed networks which lead to metric perturbations. The acoustic waves in the photon-baryon plasma sourced by these metric perturbations, when Silk damped, generate spectral distortions of the cosmic microwave background (CMB). In this work, the chemical potential distortion ($\mu$) due to scaling seed networks is computed and the accompanying Compton $y$-type distortion is estimated. The specific model of choice is the $O(N)$ nonlinear $\sigma$-model for $N\gg 1$, but the results remain the same order of magnitude for other scaling seeds. If CMB anisotropy constraints to the $O(N)$ model are saturated, the resulting chemical potential distortion $\mu \lesssim 2\times 10^{-9}$.