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, ΩGW(f_(p), T_(0))h^(2)~ Ω_(rad)h^(2)(Ω_νΩN_(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.