Cosmological perfect-fluids in f(R) gravity (original) (raw)
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We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian density F (R, R, ..., k R) have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.
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Osaka Journal of Mathematics, 2019
We show that n-dimensional perfect fluid spacetimes with divergence-free conformal curvature tensor and constant scalar curvature are generalized Robertson Walker (GRW) spacetimes; as a consequence a perfect fluid Yang pure space is a GRW spacetime. We also prove that perfect fluid spacetimes with harmonic generalized curvature tensor are, under certain conditions, GRW spacetimes. As particular cases, perfect fluids with divergence-free projective, concircular, conharmonic or quasi-conformal curvature tensor are GRW spacetimes. Finally, we explore some physical consequences of such results.
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The semiconformal curvature tensor and its divergence have been studied for perfect fluid spacetimes. It is seen, apart from other results, that the perfect fluid spacetimes with divergence-free semiconformal curvature tensor either satisfy the vacuum-like equation of state or represent FLRW cosmological model.
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General Relativity and Gravitation, 2000
We investigate shear-free, perfect fluid solutions of Einstein's field equations in which the perfect fluid satisfies a barotropic equation of state p = p(w) such that w + p = 0. We find that if the electric part of the Weyl tensor (with respect to the fluid flow) vanishes and the spacetime is not conformally flat then the fluid volume expansion is zero but the vorticity is necessarily nonzero. In addition, we show that if p = −w/3 then necessarily either the fluid expansion is zero or the fluid vorticity is zero.
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In a [Formula: see text]-dimensional Friedmann–Robertson–Walker metric, it is rigorously shown that any analytical theory of gravity [Formula: see text], where [Formula: see text] is the curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant, can be associated to a perfect-fluid stress–energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted.
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A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed in framing dark energy and dark matter in a comprehensive geometric view. Considering the concept of perfect scalars, we show that the field equations of such theories naturally contain perfect fluid terms. Specific examples are developed for the Friedman-Lemaître-Roberson-Walker metric.
Perfect fluid metrics conformal to the Schwarzschild exterior spacetime
General Relativity and Gravitation, 2012
We construct perfect fluid spacetimes by performing a conformal transformation on a non-conformally flat vacuum solution, namely the Schwarzschild exterior metric. It should be noted that conformally Ricci flat perfect fluid solutions, except those that are conformally flat, are rarely reported explicitly. In this article it is demonstrated that perfect fluid metrics conformal to the Schwarzschild exterior line element are necessarily static. The Einstein field equations for the static case reduce to a fully determined system of three differential equations in three unknowns and the conformal factor is uniquely determined in closed form. The solution is analysed for physical plausibility by establishing the positivity of the energy density and pressure profiles graphically. Additionally, the solution is observed to be causal in an appropriate limit and both the energy density and pressure is shown to be decreasing outwards towards the boundary. Finally, the weak, strong and dominant energy conditions are found to be satisfied in the region under investigation. Accordingly, the most common elementary physical conditions are met and the model is seen to be suitable for a core-envelope stellar model.
2013
In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled Einstein-massive scalar field system which rules the dynamics of a kind of pure matter in the presence of a massive scalar field and cosmological constant is proved, under the assumption that the scalar field ? is a non-decreasing function, in Robertson-Walker1 space-time; asymptotic behaviour are investigated in the case of a cosmological constant bounded from below by a strictly negative constant depending only on the massive scalar field.
The Cauchy problem for metric-affine f ( R )-gravity in the presence of perfect-fluid matter
Classical and Quantum Gravity, 2009
The Cauchy problem for metric-affine f (R)-gravityà la Palatini and with torsion, in presence of perfect fluid matter acting as source, is discussed following the well-known Bruhat prescriptions for General Relativity. The problem results well-formulated and well-posed when the perfect-fluid form of the stress-energy tensor is preserved under conformal transformations. The key role of conservation laws in Jordan and in Einstein frame is also discussed.