Gravitational waves from first order phase transitions during inflation

TL;DR

This work analyzes gravitational waves produced by first order phase transitions that occur during inflation, showing that bubble collisions dominate the GW emission while plasma turbulence and gauge-field effects are subdominant. By parameterizing the inflationary background with $H$, $ε$, and transition-specific scales ($β_n$, $Δε_n$, $r_n$) and enforcing self-consistency bounds, the authors derive a not-scale-invariant GW spectrum that accumulates over multiple transitions; each transition contributes a suppressed amplitude that scales roughly as $(H/β_n)^8 ε^2$ but can become observable if many transitions occur. The dominant signal comes from collisions of bubble walls in vacuum, with the spectrum's peak near $k≈β_n$ and a redshift evolution that takes superhorizon modes into account, enabling potential detection in the CMBR for slow transitions and with space-based interferometers (LISA, DECIGO) for large numbers of transitions. The study also shows that nucleosynthesis bounds are satisfied (e.g., in chain inflation) and provides a framework to test high-energy inflationary models with GW observations, offering distinctive signatures that could distinguish inflationary transitions from non-inflationary ones. The results indicate that a rich network of phase transitions during inflation could leave observable imprints in the early-Universe GW background, with practical implications for upcoming CMB and GW experiments.

Abstract

We study the production, spectrum and detectability of gravitational waves in models of the early Universe where first order phase transitions occur during inflation. We consider all relevant sources. The self-consistency of the scenario strongly affects the features of the waves. The spectrum appears to be mainly sourced by collisions of bubble of the new phases, while plasma dynamics (turbulence) and the primordial gauge fields connected to the physics of the transitions are generally subdominant. The amplitude and frequency dependence of the spectrum for modes that exit the horizon during inflation are different from those of the waves produced by quantum vacuum oscillations of the metric or by first order phase transitions not occurring during inflation. A moderate number of slow (but still successful) phase transitions can leave detectable marks in the CMBR, but the signal weakens rapidly for faster transitions. When the number of phase transitions is instead large, the primordial gravitational waves can be observed both in the CMBR or with LISA (marginally) and especially DECIGO. We also discuss the nucleosynthesis bound and the constraints it places on the parameters of the models.