Singular Isotropic Cosmologies and Bel-Robinson Energy

Abstract

We consider the problem of the nature and possible types of spacetime singularities that can form during the evolution of FRW universes in general relativity. We show that by using, in addition to the Hubble expansion rate and the scale factor, the Bel-Robinson energy of these universes we can consistently distinguish between the possible different types of singularities and arrive at a complete classification of the singularities that can occur in the isotropic case. We also use the Bel-Robinson energy to prove that known behaviours of exact flat isotropic universes with given singularities are generic in the sense that they hold true in every type of spatial geometry.

New isotropic and anisotropic sudden singularities

“…Note that the divergence of p with finite ρ leads to an unbounded quantity with dimensions of a velocity. Similar forms of singularity can be obtained in Friedmann universes arising as cosmological solutions of higher-order gravity theories [5,2], and other forms of finite-time singularity have been proposed in the presence of cosmological accelerations of fluid flow relative to the hypersurface-orthogonal fluid congruence in [6]. Sudden singularities are sp curvature singularities that are neither strong-curvature nor crushing [3], and their modest effects on geodesics have been studied in [7].…”

“…Here, R ab is the symmetric and trace-free component of R ab , the spatial Ricci tensor, R = R a a is the associated Ricci scalar and σ 2 = σ ab σ ab /2 is the magnitude of the shear tensor. Also, equation ( 12) combines with (6) to give…”

Talking About Singularities

“…It is based on the introduction of an invariant geometric quantity, the Bel-Robinson energy which takes into account precisely those features of the problem, related to the matter contribution, in which models still differ near the time singularity while having similar behaviours of a and H. In this way, we arrive at a complete classification of the possible cosmological singularities in the isotropic case (for more details see [24,25,26] …”

The nature of cosmological singularities in isotropic universes and braneworlds

“…This type of classification needs therefore to be refined by somehow incorporating the various matter fields into the picture. This refinement results in a more detailed classification scheme that sharpens our view of the nature of singularities [69]- [71].…”

“…The following theorem [69], [70] characterises the future singularity in phantom cos mologies irrespective of the value of the curvature k and implies that the singularities in such models can be milder than the standard all-encompassing future-collapse singulari ties and have necessarily diverging pressure. This theorem generalises and unifies previous results (cf.…”