Imprints of Reheating Dynamics on Gravitational Waves from Phase Transitions

Abstract

We investigate how perturbative reheating after inflation modifies the primordial gravitational wave (GW) spectrum generated by cosmological phase transitions. Within a specific inflationary setup, we show that the thermodynamic quantities that control the phase transition depend on the effective equation of state of the cosmological background, which is itself set by the form of the inflaton potential during reheating. Assuming reheating proceeds via perturbative dissipation of the inflaton condensate into boson or fermion pairs, we find that phase transitions taking place in this epoch generally produce GW signals that are systematically suppressed compared with the standard radiation-dominated scenario. We also identify characteristic spectral features that may arise in this case, which could serve as distinctive signatures of the modified expansion history during reheating.

Figures (5)

• Figure 1: Evolution of energy densities with scale factor, considering reheating via fermionic decay (black dotted), bosonic decay (black dashed) and bosonic scattering (black dot-dashed), for $n=4 \ (\text{top})$ and $n=6\ (\text{bottom})$. The black curves correspond to radiation energy density, while the blue one is for inflaton energy density. The top and bottom right panels show the evolution of corresponding bath temperature as a function of the scale factor. In all cases, we have fixed $T_\text{rh}=1$ TeV (as marked by the horizontal dotted line) for illustration.
• Figure 2: Bubble nucleation condition following eq. \ref{['nuc_condition']} evaluated for BM1 for different values of $n$. The horizontal lines display different values of $\gamma_{\hbox{\tiny\rm{b/f}}}$, corresponding to each choice of $n$. For the RD case, the horizontal line denotes unity.
• Figure 3: Evolution of the non-comoving bubble radius as a function of temperature for $T_\text{rh}/T_c=0.5$ (left panel) and $T_\text{rh}/T_c=0.1$ (right panel). The blue (orange) curves correspond to the fermionic (bosonic) reheating case via perturbative decay. Different line styles correspond to different $n$-values, as mentioned in the plot legend.
• Figure 4: Probability of finding a point in a false vacuum $P(T)$ for different reheating scenarios, for BM1. Horizontal grey line denotes the percolation condition $P(T)=0.71$.
• Figure 5: The GW spectra for the benchmark points listed in table \ref{['tab:benchmark_1']} and table \ref{['tab:benchmark_2']}. Coloured solid, dashed, and dotted lines indicate different inflaton potentials (see eq. \ref{['eq:inf-pot']}), which modify the redshift behaviour according to eq. \ref{['eq:rpsol']}. The black solid curve corresponds to the spectrum obtained in a standard expansion history considering RD, whereas the blue, orange and green lines denote inflaton domination with fermionic and bosonic reheating and reheating by scattering, respectively. The shaded regions depict sensitivities of upcoming and planned experiments LISA LISA:2017pwjColpi:2024xhw, ET Punturo:2010zzHild:2010id, CE LIGOScientific:2016wofReitze:2019iox and BBO Crowder:2005nr. The horizontal lines correspond to the $\Delta N_\text{eff}$ bound from different experiments (see text for details).