A Dark Matter Model with Quadratic Equation of State: Background Evolution and Structure Formation

We propose that dark matter (DM) possesses a quadratic equation of state, which becomes significant at high densities, altering the Universe's evolution during its early stages. We derive the modified background evolution equations for the Hubble parameter $H(z)$ and the DM density parameter Ωdm(z). We then perturb the governing equations to study the linear growth of matter fluctuations, computing the observable growth factor fσ₈(z). Finally, we compare the model with the latest cosmological data, including Hubble parameter $H(z)$ measurements, and growth factor fσ₈(z) data, up to $z=3$. Our results indicate that the quadratic model, while remaining consistent with background observations, offers a distinct imprint on the growth of structure, providing not only a new phenomenological avenue to address cosmological tensions but also shedding light on the nature of DM.