Geometric Perfect Fluids and Dark Side of the Universe

arxiv(2024)

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Abstract
Recently we showed that in 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 the 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 σ_1 and σ_2. To analyze this theory concerning its parameter space (σ_1, σ_2), 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 σ_2=0 case are as follows: (i) In order to have a positive energy density for the geometric fluid ρ_g, the parameter σ_1 must be negative for all dimensions up to D = 11, (ii) For a suitable choice of σ_1, 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 the 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.
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