Scalar Portal Verifiable Light Dark Matter and Correlated Gravitational Wave Signatures
The lack of signals in direct detection experiments has placed the canonical Weakly Interacting Massive Particle (WIMP) paradigm under severe tension, motivating a shift toward the sub-GeV Light Dark Matter (LDM) regime. However, realizing detectable LDM interaction rates typically requires large couplings to the visible sector, which leads to a severe thermal underabundance of the dark matter relic density within standard cosmology. Furthermore, LDM models featuring vector mediators face stringent constraints from the Cosmic Microwave Background (CMB) due to late-time energy injection. In this work, we propose a minimal scalar portal extension featuring a vector-like fermion dark matter candidate, which naturally evades CMB bounds via inherent p-wave annihilation suppression. To simultaneously achieve the correct relic density and large direct-detection couplings, we invoke a pre-Big Bang Nucleosynthesis (BBN) non-standard cosmology dominated by a stiff fluid ($w > 1/3$). The enhanced Hubble expansion during this epoch triggers an early dark matter freeze-out, successfully rescuing the asymptotic relic abundance. Crucially, this stiff pre-BBN phase heavily blue-shifts inflationary gravitational waves that re-enter the horizon prior to BBN, imprinting a distinct high-frequency tilt on the stochastic gravitational wave background. We establish a robust correlation between the non-standard expansion history, the particle physics parameters verifiable in future terrestrial direct detection experiments, and the unique gravitational wave signatures observable by forthcoming space-based interferometers like LISA and DECIGO. This framework highlights how multi-messenger observations can concurrently probe the dark sector and the pre-BBN thermal history of the Universe.