Reheating After Quintessential Inflation and Gravitational Waves

TL;DR

The paper investigates how the reheating history after quintessential inflation shapes the spectrum of primordial gravitational waves, focusing on two extreme mechanisms: gravitational particle production with a prolonged kination era and efficient instant preheating. By modeling a quintessence-informed inflationary potential and computing the GW spectrum via Bogoliubov transformations across multiple cosmic phases, it identifies three spectral branches corresponding to KD, RD, and MD horizon re-entry and shows that the KD duration—and thus the reheating efficiency—significantly boosts high-frequency GWs. Instant preheating shortens the KD period and suppresses the 100 MHz enhancement, while gravitational reheating can produce a detectable high-frequency signal within BBN constraints; these outcomes are not limited to quintessential inflation but reflect general expansion histories during inflation. The work highlights that observing or constraining GWs around $f\sim$100 MHz can reveal the thermal history of the early Universe and motivates potential tabletop high-frequency GW detectors as probes of cosmology.

Abstract

We investigate the dependence of the gravitational wave spectrum from quintessential inflation on the reheating process. We consider two extreme reheating processes. One is the gravitational reheating by particle creation in the expanding universe in which the beginning of the radiation dominated epoch is delayed due to the presence of the epoch of domination of the kinetic energy of the inflaton (kination). The other is the instant preheating considered by Felder et al. in which the Universe becomes radiation dominated soon after the end of inflation. We find that the spectrum of the gravitational waves at $\sim 100$ MHz is quite sensitive to the reheating process. This result is not limited to quintessential inflation but applicable to various inflation models. Conversely, the detection or non-detection of primordial gravitational waves at $\sim$100 MHz would provide useful information regarding the reheating process in inflation.

Figures (3)

• Figure 1: Evolution of the energy densities for gravitational reheating. The solid line is the potential energy density of $\phi$. The gray line is the kinetic energy density of $\phi$. The dotted line is the radiation and dust energy densities.
• Figure 2: Evolution of the energy densities for instant preheating. The solid line is the kinetic energy density of $\phi$, the dotted line is the energy density and the dashed line is energy density of $\psi$. In the right panel there is the era dominated by the scalar field $\chi$, because the decay rate of the field $\chi$ is low.
• Figure 3: The spectrum of gravitational waves. The left panel is in the case of the reheating by gravitational particle production. The right one is in the case of instant preheating. For comparison, we also plot the result of gravitational reheating with $R=1$.