Modern approaches to cosmological singularities

Physical Review D, 1993

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.

Classical and Quantum Gravity, 2007

We prove well-posedness of the initial value problem for the Einstein equations for spatially-homogeneous cosmologies with data at an isotropic cosmological singularity, for which the matter content is either a cosmological constant with collisionless particles of a single mass (possibly zero) or a cosmological constant with a perfect fluid having the radiation equation of state. In both cases, with a positive cosmological constant, these solutions, except possibly for Bianchi-type-IX, will expand forever, and be geodesically-complete into the future.

Il Nuovo Cimento B, 1992

This paper compares recent approaches appearing in the literature on the singularity problem for space-times with nonvanishing torsion. PACS 04.20.Cv -Fundamental problems and general formalism. PACS 04.50 -Unified field theories and other theories of gravitation.

2011

This is a thesis on general relativity. It analyzes dynamical properties of Einstein’s field equations in cosmology and in the vicinity of spacetime singularities in a number of different situations. Different techniques are used depending on the particular problem under study; dynamical systems methods are applied to cosmological models with spatial homogeneity; Hamiltonian methods are used in connection with dynamical systems to find global monotone quantities determining the asymptotic states; Fuchsian methods are used to quantify the structure of singularities in spacetimes without symmetries. All these separate methods of analysis provide insights about different facets of the structure of the equations, while at the same time they show the relationships between those facets when the different methods are used to analyze overlapping areas. The thesis consists of two parts. Part I reviews the areas of mathematics and cosmology necessary to understand the material in part II, whi...

Physical Review Letters, 2005

In this letter we investigate the nature of generic cosmological singularities using the framework developed by Uggla et al. We do so by studying the past asymptotic dynamics of general vacuum G2 cosmologies, models that are expected to capture the singular behavior of generic cosmologies with no symmetries at all. In particular, our results indicate that asymptotic silence holds, i.e., that particle horizons along all timelines shrink to zero for generic solutions. Moreover, we provide evidence that spatial derivatives become dynamically insignificant along generic timelines, and that the evolution into the past along such timelines is governed by an asymptotic dynamical system which is associated with an invariant set -the silent boundary. We also identify an attracting subset on the silent boundary that organizes the oscillatory dynamics of generic timelines in the singular regime. In addition, we discuss the dynamics associated with recurring spike formation.

2015

In this project we have performed an study of the singularities in Clasical Cosmology, considering a flat Friedmann-Lemaitre-Robertson-Walker for a linear equation of state and for a non-linear one. We have computed analitically all the possible cases, obtaining as a result a general classification for the singularities for a model with a non-linear EoS.

Physical Review D, 2002

Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated in [2], we identify two classes of peculiar interest: focusing timelike singularity solutions with the stress-energy tensor of a radiative perfect fluid (equation of state: p = 1 3 ρ) and a set of null singularity classes verifying identical properties. We consider two important applications of these results: to cosmology, as regards the possibility of solving the horizon problem with no need to resort to any inflationary scenario, and to the Strong Cosmic Censorship Hypothesis to which we propose a class of physically consistent counterexamples .

Arxiv preprint arXiv:1001.3048, 2010

In this talk we review the appearance of new types of singularities (big rip, sudden singularities. . . ) in FLRW cosmological models that have arisen on considering explanations for accelerated expansion of our universe.

2014

Latin indices from the beginning of the alphabet, a, b, c, and so on generally run over four spacetime indices 0, 1, 2, 3, where v 0 denotes the time component of the vector v a. An exception to this convention occurs in paper V and the related section in chapter 5 where they label spatial coordinate indices from 1 to 3. Greek indices from the beginning of the alphabet, α, β, γ, and so on generally run over three spatial indices 1, 2, 3, and are used to label components relative an orthonormal frame, except in paper V where they label spacetime components from 1 to 4. Greek indices from the middle of the alphabet, μ, ν, and so on are used to label spacetime coordinate components. Latin indices from the middle of the alphabet, i, j, k, and so on are used to label spatial coordinate components, or as in paper IV, components relative a group invariant frame. Repeated upper and lower indices are summed over, unless otherwise indicated. The metric has signature − + + +. Units for which 8πG = 1 and c = 1, where G is the gravitational constant and c is the speed of light, are used throughout the thesis. Vectors and tensors are represented by symbols in bold font, x, 0, g, T for example, where the dimension and rank should be discernable from the context. 2 The cosmological constant was first introduced by Einstein [23] as a way to obtain a static universe, but was abandoned by him when it was discovered that the universe is expanding, only later to be revived in light of the new observations of an accelerating universe. 3 The names dark matter/energy are a bit misleading. It may sound like dark matter is completely black, absorbing all light, but in reality it is totally transparent, not interacting with light or normal matter at all, except through its gravitational pull (and possibly through weak interactions that are of no relevance on astronomical scales). More appropriate names would be invisible matter/energy. 4 Aleksander Aleksanderoviq Friedman's last name is sometimes translated Friedmann and sometimes Friedman.

AIP Conference Proceedings, 2006

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. 1