Domain wall network: A dual solution for gravitational waves and Hubble tension?

We explore the possibility that domain wall networks generate the stochastic gravitational wave background (SGWB) observed as a strong common power-law process in the Data Release-2 of Parkes Pulsar Timing Array. We find that a broad range of parameters, specifically wall tension around σ_DW ∼ (29–414 TeV)³ and wall-decay temperature within T_d ∼ 20–257 MeV, can explain this phenomenon at a 68% credible level. Meanwhile, the same parameters could ease the Hubble tension if particles from these domain wall networks decay into dark radiation. We establish a direct analytical relationship, Ω_GW(f_p, T₀)h² ∼ Ω_radh²(Ω_vΔN_eff)², to illustrate this coincidence, underlining its importance in the underlying physics and potential applicability to a wider range of models and data. Conversely, if the common power-law process is not attributed to domain wall networks, our findings impose tight limits on the wall tension and decay temperature.