An upper limit on cosmological chiral gravitational wave background

TL;DR

The paper derives a model‑independent upper limit on the amplitude of a cosmological chiral gravitational wave background by exploiting the gravitational chiral anomaly that links $R\tilde{R}$ to lepton number production and its subsequent conversion to baryon asymmetry via electroweak sphalerons. Using a general, production‑time‑agnostic treatment for superhorizon modes and a production‑time dependent analysis for subhorizon modes, the authors relate the initial chiral GW power spectrum to the observed baryon asymmetry, yielding a bound on $h^2\Omega_{\rm GW,0}$ that tightens for high reheating temperatures and high frequencies (MHz and above). In the monochromatic approximation, the bound scales as $f_p^{-3}$ for superhorizon and $f_p^{-1}$ for subhorizon production, demonstrating a novel, model‑independent constraint on parity‑violating physics in the early Universe. This complements BBN and direct high‑frequency GW searches, providing a robust test of parity‑violating mechanisms beyond the Standard Model. If baryogenesis is dominated by non‑gravitational mechanisms, the bound further suppresses any sizable chiral GWB.

Abstract

Within the standard framework in which electroweak sphaleron processes relate lepton and baryon number, we derive an upper limit on the amplitude of a chiral gravitational wave background produced prior to the electroweak epoch. This bound is independent of the production time of chiral GWs for superhorizon modes, while it becomes sensitive to the production time for subhorizon modes. For sufficiently high reheating temperatures, the bound becomes significantly more stringent than the conventional big bang nucleosynthesis constraints at frequencies above the MHz scale, thereby providing a powerful and \emph{model-independent} probe of parity-violating physics in the early Universe.

Figures (2)

• Figure 1: The figure shows the comoving scales relevant for leptogenesis. The shaded region indicates the epoch during which electroweak sphalerons efficiently convert a lepton asymmetry into a baryon asymmetry. The conformal times $\eta_{\rm rh}$ and $\eta_{\rm EW}$ mark the end of reheating and the electroweak epoch, respectively, and together define the maximally allowed region, while $\eta_{\rm BBN}$ and $\eta_{\rm eq}$ indicate BBN and matter–radiation equality, respectively. For a GW mode with comoving wavenumber $k_p$, the initial time is set by horizon crossing, $k_p \eta_i = 1$, for super-horizon modes, while $\eta_{\rm rh}\lesssim\eta_i\lesssim\eta_{\rm EW}$ is a free parameter for the subhorizon production, e.g. $\eta_i \gg k_p^{-1}$.
• Figure 2: Constraints on total energy density of maximally chiral GWB at the present epoch by using Eq. \ref{['gw-constraint-eq']}, solid (dashed) curves for most (partially) efficient case. For comparison, we also show various detectors in high-frequency ranges (reproduced from Aggarwal:2025noe); Orange shaded region, purple and cyan curves are for the current experiment (published results), active R&D effort, and proposed experiments (concept), respectively. In this figure, the horizontal axis refers to present-day frequency $f$, which corresponds to the comoving peak frequency in our case, $f_p=k_p/2\pi$. As in \ref{['fig:scales']}, the yellow shaded region denotes the maximally allowed parameter space where our constraints are applicable. The black curve correspond to production time $\eta_i=\eta_{\rm rh,min}\simeq4.8\times10^{-9}\mathrm{Hz}^{-1}$, where $\eta_{\rm rh,min}$ refers to the time of reheating with maximally allowed reheating temperature, $T_{\rm rh,max}\simeq10^{15}\,\mathrm{GeV}$. The light-blue and brown curves correspond to $\eta_i\simeq 10^{-6}\mathrm{Hz}^{-1}$ ($T\sim10^{12}\mathrm{GeV}$) and $\eta_i=10^{-1} \, \eta_{\rm EW}\simeq4.8\times10^{3}\mathrm{Hz}^{-1}$ ($T\sim10^3\,\mathrm{GeV}$). The dotted curves denote representative sources (see main text). In particular, gauge preheating and photon-graviton conversion (EMGW), shown by the green and magenta dotted curves, correspond to very high reheating temperatures and are therefore constrained by the black solid line. See Refs. Adshead:2019igv2024-Kushwaha.Jain-PRD for details of the corresponding parameter space.