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 } .