Dark Universe inspired by the Kaluza-Klein gravity and impact on Primordial Gravitational Waves

We explore the potential implications of Kaluza-Klein (KK) gravity in unifying the dark sector of the Universe. Through dimensional reduction in KK gravity, the 5D spacetime framework can be reformulated in terms of a 4D spacetime metric, along with additional scalar and vector fields. From the 4D perspective, this suggests the existence of a tower of particle states, including KK gravitons with spin-0 and spin-1 states, in addition to the massless spin-2 gravitons of general relativity (GR). The key idea in the present paper is the analogy with superconductivity theory. By assuming a minimal coupling between an additional complex scalar field and the gauge field, a "mass" term emerges for the spin-1 gravitons. This, in turn, leads to long-range gravitational effects that could modify Newton's law of gravity through Yukawa-type corrections. Assuming an environment-dependent mass for the spin-1 graviton, near the galactic center the repulsive force from this spin-1 graviton is suppressed by an additional attractive component from Newton's constant corrections, resulting in a Newtonian-like, attraction-dominated effect. In the galaxy's outer regions, the repulsive force fades due to its short range, making dark matter appear only as an effective outcome of the dominant attractive corrections. This approach also explains dark matter's emergence as an apparent effects on cosmological scales while our model is equivalent to the scalar-vector-tensor gravity theory. Finally, we examine the impact of dark matter on the primordial gravitational wave (PGW) spectrum and show that it is sensitive to dark matter effects, providing an opportunity to test this theory through future GW observatories.