Primordial Gravitational Waves as Complementary Probe of Dark Matter Indirect Detection

We propose a novel cosmological probe of dark matter (DM) through inflationary primordial gravitational wave (GW) measurements highlighting its complementarity with traditional indirect detection. In scenarios like early matter domination (EMD), the thermal DM relic is diluted and then replenished via non-thermal production, leaving characteristic imprints on the primordial GW spectrum, inducing frequency-dependent suppressions in the GW amplitudes. By analysing signal-to-noise ratio (SNR) and employing Fisher forecast, we show that upcoming GW experiments have good potential to probe the DM parameter space involving its mass and annihilation cross-section. We show, for instance, LISA will be sensitive to DM mass range $[2\times 10^2-10^5]$ GeV. Furthermore, we identify a significant overlap of the GW missions' sensitivity reaches with the projected reach of future indirect searches like CTA with gamma rays, ANTARES, KM3NeT with neutrinos. In those overlapping regions of interests, we forecast on the GW experiments to estimate the precision of measurements. We show, for instance, that DM mass of $10^5$ GeV with an annihilation cross-section of $10^{-24}~{\rm cm}^3{\rm /s}$, and a mass of $10^4$ GeV with an annihilation cross-section of $2\times10^{-25}~{\rm cm}^3{\rm /s}$, lie within the projections of CTA. We find that whilst the former can be probed by ET with $\sim 1\%$ uncertainties, the latter can be probed by $μ$-ARES with $\sim 7 \%$ uncertainties. Similarly, DM mass of $10^5$ GeV, with cross-section $10^{-23}~{\rm cm}^3{\rm /s}$ lies within the projection of ANTARES and KM3NeT, which can be probed by ET with $\sim 1\%$ uncertainties.