Cosmological dynamics of "Unified Dark Matter" models based on perfect fluids Dinamica cosmologica di modelli di "Unified Dark Matter" basati su fluidi perfetti

The current evidence of an accelerated expansion of the universe is briefly discussed from an historical perspective and in the context of general relativity, the concept of dark energy is introduced. The presence of extra mass which doesn’t interact electromagnetically, called dark matter, is also shortly adressed. Given the fluid equation describing the evolution of the energy density ρ of the universe for FLRW models, a barotropic non-linear equation of state (EoS) P(ρ) is chosen, specifically the quadratic form P(ρ) = P0 + αρ + βρ2, already discussed by Ananda and Bruni in [1]. This particular form serves as a general approximation for every P(ρ), as it is the Taylor expansion up to the second order about ρ = 0. The EoS is studied in the high and low energy regimes and ultimately the full EoS is considered. The cosmological behaviours are discussed and compared. In detail, the change in the free parameters is explored in its consequences on closed, open and flat geometrical models of space-time, standard and phantom behaviours are found along with different possibilities for future/past singularities. The whole analysis is done using the theory of dynamical systems.