Probing Warm Inflation via Correlated Gravitational Waves from First Order Phase Transitions

TL;DR

The paper tackles the problem of distinguishing warm inflation from cold inflation by predicting gravitational waves from heating-induced first-order phase transitions during inflation and cooling-induced transitions after inflation. It develops a WI framework with a dissipative coupling $Q$ that controls the thermal bath temperature evolution, deriving GW spectra using the envelope approximation and a deformation function $S(f)$, which produces oscillatory features and a characteristic double-peak structure. Key contributions include linking the temperature evolution during heating to hPT GW signatures, predicting a second cPT peak in the post-inflation era, and identifying how observables such as $N_*$, $T_e$, $T_c$, $H_{\text{inf}}$, and $\beta_{\text{hPT}}$ map to GW amplitudes and frequencies. The findings offer a practical pathway to probe WI’s dissipative dynamics with multiband GW data, potentially distinguishing WI from CI and constraining the inflationary energy scale and thermal history of the early Universe.

Abstract

We investigate the properties of gravitational waves generated by heating induced phase transitions in warm inflation. In this scenario, the heating phase of inflation followed by subsequent cosmological cooling can trigger two associated first-order phase transitions and generate characteristic gravitational waves. The correlated gravitational wave spectral features amplitude, peak frequencies, and oscillatory behavior originate from a unified model governing both phase transitions. These signatures allow discrimination between warm and cold inflation models, and give constraint on the key parameters including the dissipative coupling strength and the inflationary energy scale, collectively illuminating early-Universe dissipative dynamics. Future gravitational wave observatories such as BBO, Ultimate DECIGO, $μ$Ares, resonant cavities, and Pulsar Timing Array experiments, will play a important role in testing these theoretical predictions.

Figures (5)

• Figure 1: This figure shows the evolution of $p(\tau)$ (top panel) and $dp(\tau)/d\tau$ (bottom panel) under different parameter values during the heating phase. The black solid line corresponds to the parameter set: $j=-2$, $n=3$, $Q_1=10$, and $\frac{\dot{\phi}_s}{3H_{\text{inf}}\phi_s}=0.01$. The blue and purple solid lines respectively represent the evolution of $p(\tau)$ (top panel) and $p'(\tau)$ (bottom panel) with different parameters.
• Figure 2: The finite-temperature potential $V(\chi)$ for first-order PTs. The black, red, and blue curves correspond to the cases $T_0 < T < T_c$, $T = T_c$, and $T > T_c$, respectively.
• Figure 3: The deformation equation is given for the parameter set $N_* = 18$, $T_e =10^{14} \, \text{GeV}$, $T_c=10^{13}\text{GeV}$ and $H_{\text{inf}} = 10^{12} \, \text{GeV}$. Here, the black dashed line represents the frequency corresponding to the Hubble scale during hPT.
• Figure 4: The energy spectrum of GWs generated by first-order PTs in the WI scenario when we select different parameter values. the GWs with an oscillatory structure at lower frequencies originate from hPT, while those at higher frequencies originate from cPT. The blue solid line represents the parameter set where $T_e=10^{14}\mathrm{GeV}$, $T_c=5\times10^{13}\mathrm{GeV}$, $H_{\text{inf}}=10^{10}\mathrm{GeV}$, $N_*=18$, $Q=5$, and the purple, red, cyan, black, and brown solid lines represent the parameter sets where $H_{\text{inf}}=5\times10^{10}\mathrm{GeV}$, $T_{c}=10^{13}\mathrm{GeV}$, $T_{e}=5\times10^{14}\mathrm{GeV}$, $Q=10$, and $N_*=34$ respectively, with all other parameters consistent with those of the blue solid line.
• Figure 5: The energy spectrum of GWs generated by first-order PTs in the WI scenario when we select $T_e=10^{14}\mathrm{GeV}$, $T_c=5\times10^{13}\mathrm{GeV}$, $H_{\text{inf}}=10^{10}\mathrm{GeV}$, $N_*=18$.