Hubble-Induced Phase Transitions: Gravitational-Wave Imprint of Ricci Reheating from Lattice Simulations

TL;DR

This work analyzes a Hubble-induced phase transition (HIPT) as a source of a post-inflationary stochastic gravitational-wave background during a stiff expansion era. Using hundreds of 3+1D lattice simulations of a non-minimally coupled spectator field, the authors derive parametric formulas for the GW spectrum, including the peak frequency, peak amplitude, integrated energy density, and a broken-power-law spectral shape, mapped to present-day observables. The results provide a fast, lattice-grounded toolkit to predict high-frequency GW signals for given model parameters and assess detectability against BBN and future detectors, with implications for connections to Higgs sector physics. The methodology and fitting formulas enable systematic exploration of reheating scenarios with extended field content and non-standard expansion histories. The study thus links early Universe dynamics to potential high-frequency gravitational-wave signals and motivates future high-frequency detector development and Higgs-related cosmology.

Abstract

Gravitational waves offer an unprecedented opportunity to look into the violent high-energy processes happening during the reheating phase of our Universe. We consider a Hubble-induced phase transition scenario as a source of a post-inflationary stochastic background of gravitational waves and analyse the main characteristics of its spectrum for the first time via numerical methods. The output of a large number of fully-fledged classical lattice simulations is condensed in a set of parametric formulas that describe key features of the gravitational wave spectrum, such as its peak amplitude and characteristic frequency, and avoid the need for further time-consuming simulations. The signal from such stochastic background is compared to the prospective sensitivity of future gravitational-wave detectors.

Figures (7)

• Figure 1: Typical output of a lattice simulation with $\nu=10$, $\lambda=10^{-4}$ and $H_{\rm kin}=10^{10} \textrm{ GeV}$ showing the power spectrum $\Delta_{\chi}(\kappa)$ of the spectator field and the GW spectrum $\Bar\Omega_{\rm GW}(\kappa)$ normalised with respect to the total energy density of the spectator field. Grey vertical lines indicate the momenta scales corresponding to the typical amplified momentum $\kappa_{\star}$ and the maximum amplified momentum $\kappa_{\rm max}$ in the tachyonic band at $z=0$. The spectra are plotted from the initial time until $z_{\rm rad}$ is reached. The orange line corresponds to the spectra measured at $z_{\rm br}$ while the red line in the second panel shows the fitted spectral shape in \ref{['eq:spectral_shape']}.
• Figure 2: Peak frequency $\kappa_{p}$ and peak amplitude $\Bar\Omega_{\rm GW,p}$ evaluated at $z_{\rm rad}$ as a function of the model parameters $(\nu, \, \lambda)$. Regarding $\Bar\Omega_{\rm GW,p}$, we have set a fiducial value of $H_{\rm kin}=10^{10} \textrm{ GeV}$. Dots indicate the output of single simulations in our scanning grid while black dashed lines display the resulting fitting formulas.
• Figure 3: Integrated GW energy density $h^2\Omega_{\rm GW, 0}$ and frequency of the peak $f_{p,0}$ at the present cosmological time as a function of the model parameters $\nu$ and $\lambda$ within the parameter space under study. For the energy-density contours, we have set a fiducial value $H_{\rm kin}=10^{10} \textrm{ GeV}$.
• Figure 4: Spectra of the SGWB signal from a HIPT as a function of the self-coupling parameter $\lambda$ for a fixed value of $\nu=10$ and $H_{\rm kin}=10^{12} \textrm{ GeV}$. Several sensitivity curves of proposed future detectors are being shown: Laser Interferometer Space Antenna (LISA) amaroseoane2017laserinterferometerspaceantennaRobson:2018ifk, Big Bang Observer (BBO) Crowder:2005nrCorbin:2005ny, UltimateDECIGO Seto:2001qfYagi:2011wgKawamura:2020pcg, Einstein Telescope (ET) Punturo:2010zzBranchesi:2023mws, and Cosmic Explorer (CE) LIGOScientific:2016wofReitze:2019iox. The grey-shaded area corresponds to the region excluded by the bound on the integrated energy-density in GWs at BBN in \ref{['eq:Neff_bound']}.
• Figure 5: Spectra of the SGWB signal from a HIPT as a function of the scale of kination $H_{\rm kin}$ for fixed values of $\nu=10$ and $\lambda=10^{-10}$. The grey-shaded area corresponds to the region excluded by the bound on the integrated energy-density in GWs at BBN in \ref{['eq:Neff_bound']}.