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 ${\sigma }_{\text{DW}}\sim (29-414,\text{TeV}{)}^3$ and wall-decay temperature within $T_d\sim 20-257,\text{MeV}$, can explain this phenomenon at a $68\mathrm{\%}$ 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, ${\mathrm{\Omega }}_{\text{GW}}(f_p,T_0)h^2\sim {\mathrm{\Omega }}_{\text{rad}}{h}^2({\mathrm{\Omega }}_{\nu }\mathrm{\Delta }{N}_{\text{eff}}{)}^2$, 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.