Cosmological Signals from Finite-Lifetime Domain Wall Networks

Abstract

We study cosmological perturbations sourced by metastable domain wall (DW) networks. Using the unconnected segment model, we derive analytic expressions for the scalar and tensor power spectra in the long-wavelength regime, finding a fixed ratio between their amplitudes during the scaling regime. These spectra grow as the network evolves, driven by the increasing correlation length and slower redshifting of the wall energy density relative to radiation, and peak at a scale set by the network's collapse time. Comparing the scalar spectrum with observational constraints, we derive bounds on the DW energy density at collapse, which we apply to $\mathbb{Z}_2$ and axion models. When these bounds are saturated, the resulting CMB $B$-mode signal can be comparable to or larger than the inflationary signal for a tensor-to-scalar ratio $r \sim 0.03$, potentially bringing it within reach of future CMB polarization experiments.