We propose a novel and comprehensive particle physics framework that addresses multiple cosmological tensions observed in recent measurements of the Hubble parameter, S8 and Lyman-α forest data. Our model, termed "SIDR+z_t" (Self Interacting Dark Radiation with transition redshift), is based on an inelastic dark matter (IDM) scenario coupled with dark radiation, governed by a dark abelian gauge symmetry. This framework naturally incorporates cold dark matter (DM), strongly interacting dark radiation (SIDR), and the interactions between these components. Simultaneously, the interacting DM-DR system can attenuate the matter power spectrum at small scales. The inelastic nature of DM provides a distinct temperature dependence for the DM-DR interaction rate determined by the mass-splitting between the inelastic dark fermions which is crucial for resolving the Ly-α discrepancies. The DR undergoes two “steps” of increased energy density when the heavier dark species freeze out and become non-relativistic, transferring their entropy to the dark radiation and enhancing ΔNeff.

In this article, we investigate the stochastic gravitational waves (GWs) spectrum, resulting from the emission of gravitons through bremsstrahlung, in the decay of particles produced by Hawking radiation. Although particle decays inevitably entail the emission of graviton due to bremsstrahlung, the associated decay width is notably suppressed due to the Planck scale suppression in the coupling of matter fields to gravitons. Consequently, the relic abundance of such GWs constituted of these gravitons undergoes a corresponding reduction. However, we demonstrate that super-heavy particles, reaching masses as high as Planck scale, can emerge naturally in the Hawking radiation of evaporating primordial black holes (PBHs) and can compensate for this suppression. In addition, we also discuss the stochastic gravitational waves constituted out of the gravitons directly radiated from such evaporating PBHs. When the super-heavy particle decays promptly after its production, then the corresponding GW spectrum remains subdominant to the one arising from direct PBH evaporation. However, if this particle is long-lived and decays after PBH evaporation, then the resulting GWs produced in these two processes have two distinct spectra with their peaks at extremely high frequencies, providing avenues for proposed ultra-high frequency gravitational wave detectors. We also show that such gravitational waves contribute significantly to substantial dark radiation, which can be probed with the enhanced sensitivity of future experiments.

Light dark matter (DM) with mass around the GeV scale faces weaker bounds from direct detection experiments. If DM couples strongly to a light mediator, it is possible to have observable direct detection rate. However, this also leads to a thermally under-abundant DM relic due to efficient annihilation into light mediators. We propose a novel scenario where a first-order phase transition (FOPT) occurring at MeV scale can restore GeV scale DM relic by changing the mediator mass sharply at the nucleation temperature. The MeV scale FOPT predicts stochastic gravitational waves with nano-Hz frequencies within reach of pulsar timing array (PTA) based experiments like NANOGrav. In addition to enhancing direct detection rate, the light mediator can also give rise to the required DM self-interactions necessary to solve the small scale structure issues of cold dark matter. The existence of light scalar mediator and its mixing with the Higgs keep the scenario verifiable at different particle physics experiments.