Geometric perfect fluids and the dark side of the universe

Abstract

Recently, we showed that in Friedman-Lemaître-Robertson-Walker (FLRW) cosmology, the contribution from higher curvature terms in any generic metric gravity theory to the energy-momentum tensor is of the perfect fluid form. Such a geometric perfect fluid can be interpreted as a fluid remaining from the beginning of the Universe, where string theory is thought to be effective. Just a short time after the beginning of the Universe, it is known that the Einstein-Hilbert action is assumed to be modified by adding all possible curvature invariants. We propose that the observed late-time accelerating expansion of the Universe can be solely driven by this geometric fluid. To support our claim, we specifically study the quadratic gravity field equations in D dimensions. We show that the field equations of this theory for the FLRW metric possess a geometric perfect fluid source containing two critical parameters σ₁ and σ₂. To analyze this theory concerning its parameter space (σ₁, σ₂), we obtain the general second-order nonlinear differential equation governing the late-time dynamics of the deceleration parameter q. Hence, using some present-day cosmological data as our initial conditions, our findings for the σ₂ = 0 case are as follows: (i) To have a positive energy density for the geometric fluid ρᵍ, the parameter σ₁ must be negative for all dimensions up to D = 11. (ii) For a suitable choice of σ₁, the deceleration parameter experiences signature changes in the past and future, and in the meantime, it lies within a negative range, which means that the current observed accelerated expansion phase of the Universe can be driven solely by the curvature of spacetime. (iii) q experiences a signature change, and as the dimension D of spacetime increases, this signature change happens at earlier and later times, in the past and future, respectively.