Primordial gravitational waves as probe of dark matter in interferometer missions: Fisher forecast and MCMC

We propose novel inflationary primordial gravitational wave (GW) spectral shapes at interferometer-based current and future GW missions to test dark matter (DM) production via gravity-portal. We consider three right-handed neutrinos (RHNs), required to generate Standard Model (SM) neutrino masses via seesaw mechanism, are produced via gravity-portal in early universe. The lightest among them is stable and is the DM candidate of the Universe. The other two RHNs decay and generate matter-antimatter asymmetry due to baryogenesis via leptogenesis. We find that future GW detectors BBO, DECIGO, ET, for instance, are able to probe DM mass for 5 × 10⁶ GeV < M_DM < 1.6 × 10⁷ GeV with a signal-to-noise ratio (SNR) > 10, along with the observed amount of baryon asymmetry due to gravitational leptogenesis for heavy RHN mass $M_{\mathcal{N}}$ \( {M}_{\mathcal{N}} \) to be around 8 × 10¹² GeV. Employing Fisher matrix forecast analysis, we identify the parameter space involving non-minimal coupling to gravity ξ, reheating temperature of the Universe T_rh and DM mass M_DM where the GW detector-sensitivities will be the maximum with the least error, along with SNR > 10. Finally, utilizing mock data for each GW detector, we perform MCMC analysis to find out the combined constraints on the various microphysics parameters. We also explore production of other cosmological relics such as QCD axion relic as DM candidate, produced via gravity-portal in early universe. We find that ET, for instance, can probe the decay constant of such DM candidates (fa) as 10⁹ GeV ≲ fa ≲ 10¹⁴ GeV for misalignment angle θ_i ∈ [0.1, π/ $\sqrt{3}$ \( \sqrt{3} \) ] and ξ = 1 with SNR > 10, whereas this range decreases with the increase of non-minimal coupling. Thus the upcoming GW missions will be able to test such non-thermal DM and baryogenesis scenarios involving very high energy scales, which is otherwise impossible to reach in particle physics experiments in laboratories.