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Impact of cosmic expansion on gravitational wave spectra from strongly supercooled first-order phase transitions

Marek Lewicki, Ville Vaskonen

Abstract

We compute the gravitational wave spectra from strongly supercooled first-order phase transitions, explicitly incorporating the evolution of the background metric across the transition from thermal inflation to radiation domination. We find that the spectral shape remains largely unchanged apart from a causality-induced super-horizon tail. However, in contrast to standard expectations, for slow transitions we show that the peak amplitude and frequency exhibit a weaker dependence on the transition rate $β$ than the usual scaling of $\propto β^{-2}$ and $\proptoβ$, respectively.

Impact of cosmic expansion on gravitational wave spectra from strongly supercooled first-order phase transitions

Abstract

We compute the gravitational wave spectra from strongly supercooled first-order phase transitions, explicitly incorporating the evolution of the background metric across the transition from thermal inflation to radiation domination. We find that the spectral shape remains largely unchanged apart from a causality-induced super-horizon tail. However, in contrast to standard expectations, for slow transitions we show that the peak amplitude and frequency exhibit a weaker dependence on the transition rate than the usual scaling of and , respectively.

Paper Structure

This paper contains 23 equations, 4 figures.

Figures (4)

  • Figure 1: The distributions of bubble radii at the moment of collision. The solid curves show the result obtained from numerical simulations by averaging over many realizations, with the bands indicating their spread. The dashed curves show the corresponding analytical estimate obtained using Eq. \ref{['eq:pRc']}. The black dashed line shows the Minkowski space result $p(R_c) = \beta e^{-\beta R_c}$.
  • Figure 2: The simulation results for the GW spectra in the dissipative bulk flow model, obtained by averaging the realisations in each frequency bin. The bands around each curve indicate the spread of the results. The black dashed curve shows the result obtained by neglecting the cosmic expansion.
  • Figure 3: The $95\%$ CL regions of the posteriors of the fit of the simulation results in the dissipative bulk flow model. Dashed lines are obtained using a simple broken power-law fit, while solid lines show the results with a double broken power law featuring a causality tail below the horizon radius scale (see Eq. \ref{['eq:fH']}).
  • Figure 4: Increase of the the peak frequency (upper panel) and suppression of the peak amplitude (lower panel) of the GW spectrum due to cosmic expansion for slow phase transitions. The data are obtained from the MCMC inference of the broken power-law fit, scaled with the results obtained neglecting the cosmic expansion.