Cosmological first-order phase transitions with large bubbles: beyond conformal fluid and flat spacetime

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Using semi-analytical models, we investigate the power spectrum of gravitational waves generated by sound waves in the plasma during a first-order phase transition in new unexplored scenarios. (i) The phase transition is accompanied by a change of the equation of state from that of pure radiation. This causes the peak of the spectrum to shift to smaller frequencies as the equation of state becomes softer and suppresses the amplitude of the power spectrum as a consequence of both sound and gravitational waves propagating across a non-conformal fluid. (ii) In addition, we investigate the novel limit of large bubbles, by which we mean that the mean bubble spacing $R_*$ is a non-negligible fraction of the Hubble length $\mathcal{H}_*^{-1}$, i.e. $R_*\mathcal{H}_* \lesssim \mathcal{O}(1)$. Since the amplitude of the gravitational wave signal increases with $R_*\mathcal{H}_*$, this is also the loud signal regime. In this regime the effects of gravity, hitherto neglected, become relevant. We carry out the calculation in cosmological perturbation theory expanding in the parameter $R_*\mathcal{H}_*$, or bubble over Hubble radius. General relativistic contributions at the next-to-leading order suppress the gravitational wave peak amplitude, with respect to the leading order contribution, by an amount that scales as $(R_*\mathcal{H}_*)^2$ and also depends on other transition parameters. This work improves the current estimation of the gravitational waves power spectrum from first order phase transitions and expands the possible scenarios of transitions that can be tested by gravitational wave detectors..

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