Reconstructing early universe evolution with gravitational waves from supercooled phase transitions

TL;DR

This work analyzes gravitational waves from supercooled cosmological first-order phase transitions and how inefficient reheating can yield an early matter-dominated epoch that leaves a distinctive imprint on the stochastic GW background. Using two GW signal templates—geometric (spectral) and thermodynamical—and Fisher-matrix forecasts for LISA and Einstein Telescope, it assesses the reconstructability of both spectral and underlying thermodynamical parameters, including the decay rate $\Gamma_{\varphi}$. The results show that, for strong transitions, the modified expansion history after the transition can be probed via the low-frequency tilt of the spectrum, and the (weakly coupled) decay rate can be inferred in favorable cases, linking GW observations to underlying beyond-Standard-Model physics such as classically scale-invariant scenarios. This provides a novel cosmological probe of reheating dynamics and offers a complementary window to collider experiments for exploring weakly interacting sectors.

Abstract

We study gravitational waves from supercooled cosmological first-order phase transitions. If such a transition is followed by inefficient reheating, the evolution history of the universe is modified by a period of early matter domination. This leaves an imprint on the predicted gravitational-wave spectra. Using Fisher analysis we show the parameter space in reach of upcoming gravitational wave observatories where reheating can be probed due to its impact on the stochastic background produced by the transition. We use both the simplified geometric parametrisation and the thermodynamical one explicitly including the decay rate of the field undergoing the transition as a parameter determining the spectrum. We show the expansion history following the transition can be probed provided the transition is very strong which is naturally realised in classically scale invariant models generically predicting supercooling. Moreover, in such a scenario the decay rate of the scalar undergoing the phase transition, a parameter most likely inaccessible to accelerators, can be determined through the spectrum analysis.

Figures (5)

• Figure 1: Evolution of the energy density of the scalar $\rho_\varphi$ (dashed lines) and the radiation $\rho_R$ (dotted lines) for different values of the scalar decay rate $\Gamma_{\varphi}$ indicated with different colours. The densities are normalised to the overall energy scale $\Delta V=\rho_{\rm max}$. The vertical dotted lines to the left show the scale factor $a_{\rm max}$ for which the maximal temperature is reached, while the vertical dot-dashed lines indicate the scale factor $a_{\rm eq}$ of reheating for which $\rho_\varphi=\rho_R$ in each case.
• Figure 2: Examples of spectra with fixed peak amplitude $\Omega_p=10^{-9}$, and various peak frequencies $f_p$ indicated by colour (see the legend). The breaking frequencies $f_*$ are marked by vertical dashed lines in respective colours. LISA power-law integrated sensitivity curve (PLS) is shown with a solid black line in the top panel while the bottom panel features the PLS for ET.
• Figure 3: The solid lines show example spectra for the three benchmark values for $\Gamma_{\varphi}=H_*,\ 0.1H_*,\ 0.01H_*$ as indicated by the colours. Peak frequencies are marked with dash-dotted vertical lines in respective colours while the solid black lines correspond to the PLS sensitivity curves. In the top panel, the parameters are fixed to $T_{\text{max}}=10^5\text{ GeV}$ and $\beta/H_*=10$ with the PLS curve corresponding to LISA while in the bottom panel $T_{\text{max}}=10^9\text{ GeV}$ and $\beta/H_*=10$ and the PLS curve corresponds to ET.
• Figure 4: Relative uncertainties in the reconstruction of geometrical parameters with LISA (top panel) and ET (bottom panel), for the low-frequency slope $d=3$ and $d=1$ (see eq. \ref{['eq:spectrum_spectral_parametrization']}). Solid, dashed and dotted blue lines correspond to the normalised uncertainties of $1\%$, $10\%$ and $100\%$ respectively. The black solid line corresponds to ${\rm SNR}=10$ for the signal with d=3 for comparison. The stars in the top and bottom panels represent parameters of the spectra from the top and bottom panels of figure \ref{['fig_plot_spectra_d']}.
• Figure 5: Reconstruction of thermodynamical parameters using LISA (top panel) and ET (bottom panel). The dashed contours correspond to a 10$\%$ relative uncertainty in reconstruction while the solid contours correspond to ${\rm SNR}=10$. The colour of the contours indicates one of the three benchmark values for $\Gamma_{\varphi}/H_*=1,\ 0.1, {\rm and } \ 0.01$. The stars represent parameters of the spectra from the corresponding panels in figure \ref{['fig_plot_spectra_gmma']}.