Inflationary Gravitational Waves as a probe of the unknown post-inflationary primordial Universe

TL;DR

This paper investigates how multiple phase transitions in the post-inflationary universe's equation of state affect the spectrum of primordial gravitational waves, providing potential signals detectable by future GW observatories.

Contribution

It introduces a model with multiple sharp transitions in the post-inflationary equation of state and analyzes their impact on the gravitational wave spectrum, identifying detectable parameter regions.

Findings

Multiple phase transitions can produce distinctive features in the GW spectrum.

Certain combinations of EoS parameters yield signals within the sensitivity of upcoming detectors.

The model constrains the post-inflationary dynamics consistent with current observational limits.

Abstract

One of the key predictions of the standard inflationary paradigm is the quantum mechanical generation of the transverse and traceless tensor fluctuations due to the rapid accelerated expansion of space, which later constitute a stochastic background of primordial gravitational waves (GWs). The amplitude of the (nearly) scale-invariant inflationary tensor power spectrum at large scales provides us with crucial information about the energy scale of inflation in the case of the minimal inflaton coupling to gravity. Furthermore, the spectral energy density, $\Omega_{_{\rm GW}}(f)$, of the GWs at sufficiently small scales (or, large frequencies $f$) serves as an important observational probe of post-inflationary primordial dynamics. In fact, the small-scale spectral tilt, $n_{_{\rm GW}} = \frac{{\rm d}\log{\Omega_{_{\rm GW}}}}{{\rm d}\log{f}}$, of the spectral energy density of GWs is sensitive to the (unknown) post-inflationary equation of state (EoS), $w$, of the universe; with a softer EoS ($w < 1/3$) leading to a red tilt: $n_{_{\rm GW}} < 0$, while a stiffer EoS ($w > 1/3$) resulting in a blue tilt: $n_{_{\rm GW}} > 0$. The post-inflationary dynamics, however, is generically expected to be quite complex, potentially involving a number of distinct phases. Hence, in this work, we discuss the possibility of multiple sharp transitions, namely $w_1 \to w_2 \to w_3 \to ... \to w_n$, in the EoS of the post-inflationary universe and compute the corresponding spectral energy density of the inflationary GWs. We explicitly determine the region of the parameter space $\lbrace{ w_1, \, w_2, \, w_3, ..., w_n\rbrace}$ which leads to a potentially detectable signal in the upcoming GW detectors, without violating the current constraints.