Domain Wall Network: A Dual Solution for Gravitational Waves and Hubble Tension?

Abstract

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 $\sigma_{\textrm{DW}} \sim (29-414 , \textrm{TeV})^3$ and wall-decay temperature within $T_d \sim 20-257 , \textrm{MeV}$, 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, $\Omega_{\textrm{GW}}(f_p,T_0) h^2 \sim \Omega_{\textrm{rad}} h^2 ( \Omega_\nu \Delta N_{\textrm{eff}})^2$, 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.