Cosmological models with flat spatial geometry

Abstract

Abstract. The imposition of symmetries or special geometric properties on submanifolds is less restrictive than to impose them in the full space-time. Starting from this idea, in this paper we study irrotational dust cosmological models in which the geometry of the hypersurfaces generated by the fluid velocity is flat, which supposes a relaxation of the restrictions imposed by the Cosmological Principle. The method of study combines covariant and tetrad methods that exploits the geometrical and physical properties of these models. This procedure will allow us to determine all the space-times within this class as well as to study their properties. Some important consequences and applications of this study are also discussed.

Shear-free perfect fluids with a barotropic equation of state in general relativity: the present status

“…The subsequent time evolutions of this equation will be calculated using (30)(31)(32) and (83,84). The first element of this sequence, ∂ 0 (79), is given by (cf.…”

“…Since then the conjecture has been proved also in a large number of special cases, such as dp/dµ = − 1 3 [10,21,29,36]; θ = θ(ω) [32]; Petrov types N [2] and III [3,4]; the existence of a conformal Killing vector parallel to the fluid flow [9]; the Weyl tensor having either a divergence-free electric part [39], or a divergence-free magnetic part, in combination with an equation of state which is of the γ-law type [38] or which is sufficiently generic [5], and in the case where the Einstein field equations are linearised about a FLRW background [25] . A major step has been achieved recently by the second author [30] proving the conjecture for an arbitrary γ-law equation of state (except for the cases γ − 1 = − 1 5 , − 1 6 , − 1 11 , − 1 21 , 1 15 , 1 4 ) and a vanishing cosmological constant.…”

Equilibrium configurations in the dynamics of irrotational dust matter

“…As in previous cases we start from covariant spacetime characterizations. For Bianchi I models two such characterizations follow from [37]. The first one is determined by the vanishing of the spatial covariant derivative of the shear D a σ bc = 0 .…”

“…As we can see, this question depends only on the form of the different terms that make up the tensor F 1 αβ [see Eq. (37)]. The explicit expressions for its components are given in Appendix A, where the combination of constraints CC ab has been chosen in the following way: CC + = CC − = CC 1 = 0, and [see Eqs.…”

Covariant velocity and density perturbations in quasi-Newtonian cosmologies

“…(Further developments of the approach are given in [11][12][13].) Applications of a covariant approach to 'silent' universes [14][15][16], to nonlinear gravitational radiation [17,18], and to non-accelerating fluid models [19,20] reveal the existence of crucial integrability conditions. The covariant characterization of scalar, vector and tensor perturbations also relies on such an approach [21][22][23][24][25].…”