Morphology of Inflationary Gravitational Wave Spectra imprinted by a Sequence of Post-Inflationary Epochs $via$ $\mathrm{GWInSpect}$

Abstract

The expansion history of the Universe prior to Big Bang Nucleosynthesis (BBN) remains largely unconstrained. The high-energy post-inflationary era may involve multiple distinct epochs, each characterized by a different equation of state (EoS). A key prediction of inflation is the generation of tensor perturbations that later manifest as a stochastic background of primordial gravitational waves (GWs). The large-scale amplitude and small-scale spectral tilt ($n_{\mathrm{GW}}$) of these GWs encode the inflationary energy scale and the subsequent expansion history, respectively. A soft post-inflationary EoS ($w<1/3$) yields red-tilted GW spectra ($n_{\mathrm{GW}}<0$), while a stiff EoS ($w>1/3$) results in a blue-tilt ($n_{\mathrm{GW}}>0$). In our previous work [arXiv:2407.07956], we developed an analytical framework for computing the GW spectral energy density, ${\Omega }_{\mathrm{GW}}(f)$, for multiple post-inflationary transitions ($w_1\to w_2\to \cdots \to w_n\to 1/3$), focusing on the parameter space relevant for future GW observations. In this paper, we extend that framework to systematically investigate the $morphologicaldiversity$ of inflationary GW spectra generated by multi-epoch post-inflationary histories. Remaining model agnostic, we demonstrate that a wide variety of spectral shapes, ranging from convex and concave monotonic profiles to multi-peaked non-monotonic spectra, can naturally emerge depending on the sequence and duration of these epochs. We also introduce GWInSpect, a publicly available Python package that computes ${\Omega }_{\mathrm{GW}}(f)$ for arbitrary sequences of EoS transitions, providing a practical tool to study the pre-BBN expansion history of the Universe.

Comments: 17 pages (excluding references), 7 captioned figures, Revised version: GWInSpect is now a python package (link provided, tutorial notebook added), comments and queries are welcome