Gravitational waves from chiral phase transition in a conformally extended standard model

The gravitational wave (GW) background produced at the cosmological chiral phase transition in a conformal extension of the standard model is studied. To obtain the bounce solution of coupled field equations we implement an iterative method. We find that the corresponding $O(3)$ symmetric Euclidean action $S_3$ divided by the temperature $T$ has a simple behavior near the critical temperature $T_C$: $S_3\mathrm{/}T\propto (1-T\mathrm{/}{T}_C{)}^{-\gamma }$, which is subsequently used to determine the transition’s inverse duration $\beta$ normalized to the Hubble parameter $H$. It turns out that $\beta \mathrm{/}H\gtrsim {10}^3$, implying that the sound wave period ${\tau }_{\text{sw}}$ as an active GW source, too, can be much shorter than the Hubble time. We therefore compute ${\tau }_{\text{sw}}H$ and use it as the reduction factor for the sound wave contribution. The signal-to-noise ratio (SNR) for Deci-Hertz Interferometer Gravitational Wave Observatory (DECIGO) and Big Bang Observer (BBO) is evaluated, with the result: SNR${}^{\text{DECIGO}}\lesssim 1.2$ and SNR${}^{\text{BBO}}\lesssim 12.0$ for five years observation, from which we conclude that the GW signal predicted by the model in the optimistic case could be detected at BBO.