Future singularities of isotropic cosmologies

Cotsakis, Spiros; Klaoudatou, Ifigeneia

doi:10.1016/j.geomphys.2004.12.012

Cited by 63 publications

(49 citation statements)

References 27 publications

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“…Then according to Theorem 2.1, there is a finite time t 1 for which H fails to be integrable on the proper time interval [t 1 , ∞). In turn, this non-integrability of the expansion rate H can be implemented in different ways and we arrive at the following result for the types of future singularities that can occur in isotropic universes (see [4] The character of the singularities in this theorem is expected to be in a sense somewhat milder than standard all-encompassing big-crunch type ones predicted by the Hawking-Penrose singularity theorems. For instance, those satisfying condition S1 may correspond to 'sudden' singularities located at the right end (say t s ) at which H is defined and finite but the left limit, lim τ →t…”

Section: Theorem 21 (Completeness Of Friedmann Universes) Every Globmentioning

confidence: 95%

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Modern approaches to cosmological singularities

Cotsakis

Klaoudatou

2005

J. Phys.: Conf. Ser.

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Abstract. We review recent work and present new examples about the character of singularities in globally and regularly hyperbolic, isotropic universes. These include recent singular relativistic models, tachyonic and phantom universes as well as inflationary cosmologies. IntroductionAn important question eventually arising in every study of the global geometric and physical properties of the universe is that of deciding whether or not the resulting model is geodesically complete. Geodesic completeness is associated with an infinite proper time interval of existence of privileged observers and implies that such a universe will exist forever. Its negation, geodesic incompleteness or the existence of future and/or past singularities of a spacetime, is often connected to an 'end of time' for the whole universe modeled by the spacetime in question. By now there exist simple singular cosmological models of all sorts, not incompatible with recent observations, in which an all-encompassing singularity features as such a catastrophic event.It is well known that in general relativity there are a number of rigorous theorems predicting the existence of spacetime singularities in the form of geodesic incompleteness under certain geometric and topological conditions (see, e.g., [1] for a recent review). These conditions can be interpreted as restrictions on the physical matter content as well as plausibility assumptions on the causal structure of the spacetime in question. Because all these assumptions are not unreasonable, the singularity theorems predicting the existence of spacetime singularities in cosmology and gravitational collapse have become standard ingredients of the current cosmological theory.However, such existence results cannot offer any clue about the generic nature of the singularities they predict. In addition, there are new completeness theorems (cf. [2]) which say that under equally general geometric assumptions, generic spacetimes are future (or past) geodesically complete. Among the chief hypotheses of the completeness theorems, except the usual causality ones also present in the singularity theorems, is the assumption that the space slice does not 'vibrate' too much as it moves forward (or backward) in time, and also the assumption that space does not curve itself too much in spacetime. It may well be that cosmological models in a generic sense are only mildly singular or even complete. It remains thus a basic open problem to decide about the character of the cosmological singularities predicted by the singularity theorems.In preparing to tackle such basic open questions more information is required, and one feels that perhaps different techniques are needed which the singularity theorems cannot provide. We

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Section: Theorem 21 (Completeness Of Friedmann Universes) Every Globmentioning

confidence: 95%

“…Despite these negative features, one can easily construct complete as well as singular models (see [4] for more examples of this sort). Consider a Friedmann universe filled with a generalized Chaplygin gas with equation of state given by [10] …”

Section: Tachyonic Cosmologiesmentioning

confidence: 99%

Modern approaches to cosmological singularities

Cotsakis

Klaoudatou

2005

J. Phys.: Conf. Ser.

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“…As discussed in [4], Theorem (1.1) describes possible time singularities that are met in FRW universes having a Hubble parameter that behaves like S 1 or S 2 or S 3 . Although such a classification is a first step to clearly distinguish between the various types of singularities that can occur in such universes, it does not bring out some of the essential features of the dynamics that differ from singularity to singularity.…”

Section: Classificationmentioning

confidence: 99%

“…In [4] we derived necessary conditions for the existence of finite time singularities in globally and regularly hyperbolic isotropic universes, and provided first evidence for their nature based entirely on the behaviour of the Hubble parameter H =ȧ/a. This result may be summarized as follows: Condition S 2 describes a future blow up singularity and condition S 3 may lead to a sudden singularity (where H remains finite), but for this to be a genuine type of singularity, in the sense of geodesic incompleteness, one needs to demonstrate that the metric is non-extendible to a larger interval.…”

Section: Introductionmentioning

confidence: 99%

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Singular Isotropic Cosmologies and Bel-Robinson Energy

Cotsakis¹,

Klaoudatou²

2006

AIP Conference Proceedings

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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.

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Big-Bang Problem

Calcagni

2017

Classical and Quantum Cosmology

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Future singularities of isotropic cosmologies

Cited by 63 publications

References 27 publications

Modern approaches to cosmological singularities

Modern approaches to cosmological singularities

Singular Isotropic Cosmologies and Bel-Robinson Energy

Big-Bang Problem

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