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 S3 divided by the temperature T has a simple behavior near the critical temperature TC: S3/T∝(1−T/TC)−γ, which is subsequently used to determine the transition's inverse duration β normalized to the Hubble parameter H. It turns out that β/H≳103, implying that the sound wave period τsw as an active GW source, too, can be much shorter than the Hubble time. We therefore compute τswH 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: SNRDECIGO≲1.2 and SNRBBO≲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.