Domain Wall Cosmology: From De Sitter Fragmentation to Gravitational Wave Signatures

ABSTRACT:We present a cosmological model in which an initially symmetric de Sitter phase undergoes spontaneous localization through symmetry breaking in a two-field scalar sector. The instability dynamically generates a metastable domain wall network whose energy density scales as ρ_DW ∝ H, leading to a modified Friedmann equation containing a term linear in H. This transient modification addresses the Hubble tension while producing a correlated stochastic gravitational wave background in the nHz frequency range observable by pulsar timing arrays. We derive the full background equations from a fundamental action, perform a covariant second-order perturbation analysis using the ADM formalism, and demonstrate that isocurvature modes decay exponentially. The model contains ΛCDM as a continuous limit and predicts a distinctive correlated observational signature absent in standard cosmology.