Energy Conditions and Supernovae Observations

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors on physical grounds. We show that in the standard Friedmann-Lemaitre-Robertson-Walker approach to cosmological modelling where the equation of state of the cosmological fluid is unknown, the energy conditions provide model-independent bounds on the behavior of the distance modulus of cosmic sources as a function of the redshift. We use both the gold and the legacy samples of current type Ia supenovae to carry out a model-independent analysis of the energy conditions violation in the context of standard cosmology.Comment: 4 pages, 2 figures; v2: References added, misprints corrected, published in Phys.Rev.D in the present for

Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1,1...1], [21...1], [31\ldots 1], [z\bar{z}1...1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.Comment: 14 pages, LaTeX, replaced due to a LaTex erro

Lookback time bounds from energy conditions

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors on physical grounds. We show that in the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) approach to cosmological modeling, where the energy and matter components of the cosmic fluid are unknown, the energy conditions provide model-independent bounds on the behavior of the lookback time of cosmic sources as a function of the redshift for any value of the spatial curvature. We also confront such bounds with a lookback time sample which is built from the age estimates of 32 galaxies lying in the interval $0.11 \lesssim z \lesssim 1.84$ and by assuming the total expanding age of the Universe to be $13.7 \pm 0.2$ Gyr, as obtained from current cosmic microwave background experiments. In agreement with previous results, we show that all energy conditions seem to have been violated at some point of the recent past of cosmic evolution.Comment: 7 pages, 3 figures. v2: Minor changes, published in Phys.Rev.D in the present for

Causal Anomalies in Kaluza-Klein Gravity Theories

Causal anomalies in two Kaluza-Klein gravity theories are examined, particularly as to whether these theories permit solutions in which the causality principle is violated. It is found that similarly to general relativity the field equations of the space-time-mass Kaluza-Klein (STM-KK) gravity theory do not exclude violation of causality of G\"odel type, whereas the induced matter Kaluza-Klein (IM-KK) gravity rules out noncausal G\"odel-type models. The induced matter version of general relativity is shown to be an efficient therapy for causal anomalies that occurs in a wide class of noncausal geometries. Perfect fluid and dust G\"odel-type solutions of the STM-KK field equations are studied. It is shown that every G\"odel-type perfect fluid solution is isometric to the unique dust solution of the STM-KK field equations. The question as to whether 5-D G\"odel-type non-causal geometries induce any physically acceptable 4-D energy-momentum tensor is also addressed.Comment: 16 page. LaTex file. To appear in Int. J. Mod. Phys. A (1998

Energy Conditions and Cosmic Acceleration

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors $T_{\mu\nu}$ in different frameworks, and to derive general results that hold in a variety of general contexts on physical grounds. We show that in the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) approach, where the equation of state of the cosmological fluid is unknown, the energy conditions provide model-independent bounds on the behavior of the distance modulus of cosmic sources as a function of the redshift for any spatial curvature. We use the most recent type Ia supernovae (SNe Ia) observations, which include the new Hubble Space Telescope SNe Ia events, to carry out a model-independent analysis of the energy conditions violation in the context of the standard cosmology. We show that both the null (NEC), weak (WEC) and dominant (DEC) conditions, which are associated with the existence of the so-called phantom fields, seem to have been violated only recently ($z \lesssim 0.2$), whereas the condition for attractive gravity, i.e., the strong energy condition (SEC) was firstly violated billions of years ago, at $z \gtrsim 1$.Comment: 6 pages, 3 figures. v2: References added, misprints corrected, published in Phys.Rev.D in the present for

Generalized Chaplygin gas model, supernovae and cosmic topology

In this work we study to which extent the knowledge of spatial topology may place constraints on the parameters of the generalized Chaplygin gas (GCG) model for unification of dark energy and dark matter. By using both the Poincar\'e dodecahedral and binary octahedral spaces as the observable spatial topologies, we examine the current type Ia supernovae (SNe Ia) constraints on the GCG model parameters. We show that the knowledge of spatial topology does provide additional constraints on the $A_s$ parameter of the GCG model but does not lift the degeneracy of the $\alpha$ parameter.Comment: Revtex 4, 8 pages, 10 figures, 1 table; version to match the published on

Energy conditions bounds and their confrontation with supernovae data

The energy conditions play an important role in the understanding of several properties of the Universe, including the current accelerating expansion phase and the possible existence of the so-called phantom fields. We show that the integrated bounds provided by the energy conditions on cosmological observables such as the distance modulus $\mu(z)$ and the lookback time $t_L(z)$ are not sufficient (nor necessary) to ensure the local fulfillment of the energy conditions, making explicit the limitation of these bounds in the confrontation with observational data. We recast the energy conditions as bounds on the deceleration and normalized Hubble parameters, obtaining new bounds which are necessary and sufficient for the local fulfillment of the energy conditions. A statistical confrontation, with $1\sigma-3\sigma$ confidence levels, between our bounds and supernovae data from the gold and combined samples is made for the recent past. Our analyses indicate, with $3\sigma$ confidence levels, the fulfillment of both the weak energy condition (WEC) and dominant energy condition (DEC) for $z \leq 1$ and $z \lesssim 0.8$, respectively. In addition, they suggest a possible recent violation of the null energy condition (NEC) with $3\sigma$, i.e. a very recent phase of super-acceleration. Our analyses also show the possibility of violation of the strong energy condition (\textbf{SEC}) with $3\sigma$ in the recent past ($z \leq 1$), but interestingly the $q(z)$-best-fit curve crosses the SEC-fulfillment divider at $z \simeq 0.67$, which is a value very close to the beginning of the epoch of cosmic acceleration predicted by the standard concordance flat $\Lambda$CDM scenario.Comment: 7 pages, 3 figures. V2: Version to appear in Phys.Rev.D, analyses extended to 1sigma, 2sigma and 3sigma confidence levels, references added, minors change

Godel-type Universes in String-inspired Charged Gravity

We consider a string-inspired, gravitational theory of scalar and electromagnetic fields and we investigate the existence of axially-symmetric, G\"{o}del-type cosmological solutions. The neutral case is studied first and an "extreme" G\"{o}del-type rotating solution, that respects the causality, is determined. The charged case is considered next and two new configurations for the, minimally-coupled to gravity, electromagnetic field are presented. Another configuration motivated by the expected distribution of currents and charges in a rotating universe is studied and shown to lead to a G\"{o}del-type solution for a space-dependent coupling function. Finally, we investigate the existence of G\"{o}del-type cosmological solutions in the framework of the one-loop corrected superstring effective action and we determine the sole configuration of the electromagnetic field that leads to such a solution. It turns out that, in all the charged cases considered, Closed Timelike Curves do appear and the causality is always violated.Comment: 26 pages, LaTex file, a few comments and references added, version to appear in Physical Review

A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that in which the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we reexamine the classification of the second order symmetric tensors in 5--D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in 5-dimensional space-times. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional spaces from the classification on 4-dimensional spaces. This is important in the context of 11--D supergravity and 10--D superstrings.Comment: 12 pages, to appear in Mod. Phys. Lett. A (2003) in the present for

An anisotropic cosmological model with isotropic background radiation

We present an exact solution of Einstein equations that describes a Bianchi type III spacetime with conformal expansion. The matter content is given by an anisotropic scalar field and two perfect fluids representing dust and isotropic radiation. Based on this solution, we construct a cosmological model that respects the evolution of the scale factor predicted in standard cosmology.Comment: 4 pages; contribution to the Proceedings of the 24th Spanish Relativity Meeting (ERE2001