Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds

We refine and extend a programme initiated by one of the current authors [Science 276 (1997) 88; Phys. Rev. D56 (1997) 7578] advocating the use of the classical energy conditions of general relativity in a cosmological setting to place very general bounds on various cosmological parameters. We show how the energy conditions can be used to bound the Hubble parameter H(z), Omega parameter Omega(z), density rho(z), distance d(z), and lookback time T(z) as (relatively) simple functions of the redshift z, present-epoch Hubble parameter H_0, and present-epoch Omega parameter Omega_0. We compare these results with related observations in the literature, and confront the bounds with the recent supernova data.Comment: 21 pages, 2 figure

Cosmological milestones and energy conditions

Until recently, the physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the "big bang", and possibly a "big crunch". However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with "big rips" and "sudden singularities" added to the mix, as well as renewed interest in non-singular cosmological events such as "bounces" and "turnarounds". In this talk, we present an extensive catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, using generalized power series, purely kinematical definitions of these cosmological events are provided in terms of the behaviour of the scale factor a(t). The notion of a "scale-factor singularity" is defined, and its relation to curvature singularities (polynomial and differential) is explored. Second, dynamical information is extracted by using the Friedmann equations (without assuming even the existence of any equation of state) to place constraints on whether or not the classical energy conditions are satisfied at the cosmological milestones. Since the classification is extremely general, and modulo certain technical assumptions complete, the corresponding results are to a high degree model-independent.Comment: 8 pages, 1 table, conference proceedings for NEB XII conference in Nafplio, Greec

The Hubble series: Convergence properties and redshift variables

In cosmography, cosmokinetics, and cosmology it is quite common to encounter physical quantities expanded as a Taylor series in the cosmological redshift z. Perhaps the most well-known exemplar of this phenomenon is the Hubble relation between distance and redshift. However, we now have considerable high-z data available, for instance we have supernova data at least back to redshift z=1.75. This opens up the theoretical question as to whether or not the Hubble series (or more generally any series expansion based on the z-redshift) actually converges for large redshift? Based on a combination of mathematical and physical reasoning, we argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z>1, corresponding to a universe less than half its current size. Furthermore, we shall argue on theoretical grounds for the utility of an improved parameterization y=z/(1+z). In terms of the y-redshift we again argue that the radius of convergence of any series expansion in y is less than or equal to 1, so that y-based expansions are likely to be good all the way back to the big bang y=1, but that y-based expansions must break down for y<-1, now corresponding to a universe more than twice its current size.Comment: 15 pages, 2 figures, accepted for publication in Classical and Quantum Gravit

Effective refractive index tensor for weak field gravity

Gravitational lensing in a weak but otherwise arbitrary gravitational field can be described in terms of a 3 x 3 tensor, the "effective refractive index". If the sources generating the gravitational field all have small internal fluxes, stresses, and pressures, then this tensor is automatically isotropic and the "effective refractive index" is simply a scalar that can be determined in terms of a classic result involving the Newtonian gravitational potential. In contrast if anisotropic stresses are ever important then the gravitational field acts similarly to an anisotropic crystal. We derive simple formulae for the refractive index tensor, and indicate some situations in which this will be important.Comment: V1: 8 pages, no figures, uses iopart.cls. V2: 13 pages, no figures. Significant additions and clarifications. This version to appear in Classical and Quantum Gravit

High-Redshift Cosmography

We constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires a very minimal set of assumptions (namely to specify a metric) and does not rely on the dynamical equations for gravity. On the data side, we consider the most recent compilations of Supernovae and Gamma Ray Bursts catalogues. This allows to further extend the cosmographic fit up to $z = 6.6$, i.e. up to redshift for which one could start to resolve the low z degeneracy among competing cosmological models. In order to reliably control the cosmographic approach at high redshifts, we adopt the expansion in the improved parameter $y = z/(1+z)$. This series has the great advantage to hold also for $z > 1$ and hence it is the appropriate tool for handling data including non-nearby distance indicators. We find that Gamma Ray Bursts, probing higher redshifts than Supernovae, have constraining power and do require (and statistically allow) a cosmographic expansion at higher order than Supernovae alone. Exploiting the set of data from Union and GRBs catalogues, we show (for the first time in a purely cosmographic approach parametrized by deceleration $q_0$, jerk $j_0$, snap $s_0$) a definitively negative deceleration parameter $q_0$ up to the 3$\sigma$ confidence level. We present also forecasts for realistic data sets that are likely to be obtained in the next few years.Comment: 16 pages, 6 figures, 3 tables. Improved version matching the published one, additional comments and reference

Entropy bounds in terms of the w parameter

In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP 1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an entropy bound for equilibrium uncollapsed matter using only classical general relativity, basic thermodynamics, and the Unruh effect. An odd feature of that bound, S <= A/2, was that the proportionality constant, 1/2, was weaker than that expected from black hole thermodynamics, 1/4. In the current article we strengthen the previous results by obtaining a bound involving the (suitably averaged) w parameter. Simple causality arguments restrict this averaged parameter to be <= 1. When equality holds, the entropy bound saturates at the value expected based on black hole thermodynamics. We also add some clarifying comments regarding the (net) positivity of the chemical potential. Overall, we find that even in the absence of any black hole region, we can nevertheless get arbitrarily close to the Bekenstein entropy.Comment: V1: 14 pages. V2: One reference added. V3: This version accepted for publication in JHE

Stable Gravastars of Anisotropic Dark Energy

Dynamical models of prototype gravastars made of phantom energy are constructed, in which an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-\gamma)\sigma$ divides the whole spacetime into two regions, the internal region filled with a dark energy (or phantom) fluid, and the external Schwarzschild region. It is found that in some cases the models represent the "bounded excursion" stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes or normal stars. In the phase space, the region for the "bounded excursion" gravastars is very small in comparison to that of black holes, but not empty, as found in our previous papers. Therefore, although the existence of gravastars can not be completely excluded from current analysis, the opposite is not possible either, that is, even if gravastars exist, they do not exclude the existence of black holes.Comment: 35 pages, 43 figures, added some clarifying texts and corrected some typos, accepted for publication in JCA

How the Charge Can Affect the Formation of Gravastars

In recent work we physically interpreted a special gravastar solution characterized by a zero Schwarzschild mass. In fact, in that case, none gravastar was formed and the shell expanded, leaving behind a de Sitter or a Minkowski spacetime, or collapsed without forming an event horizon, originating what we called a massive non-gravitational object. This object has two components of non zero mass but the exterior spacetime is Minkowski or de Sitter. One of the component is a massive thin shell and the other one is de Sitter spacetime inside. The total mass of this object is zero Schwarzschild mass, which characterizes an exterior vacuum spacetime. Here, we extend this study to the case where we have a charged shell. Now, the exterior is a Reissner-Nordstr\"om spacetime and, depending on the parameter $\omega=1-\gamma$ of the equation of state of the shell, and the charge, a gravastar structure can be formed. We have found that the presence of the charge contributes to the stability of the gravastar, if the charge is greater than a critical value. Otherwise, a massive non-gravitational object is formed for small charges.Comment: 17 pages and 7 figures, several typos corrected, accepted for publication in JCA

Non-perturbative results for the luminosity and area distances

The notion of luminosity distance is most often defined in purely FLRW (Friedmann-Lemaitre-Robertson-Walker) cosmological spacetimes, or small perturbations thereof. However, the abstract notion of luminosity distance is actually much more robust than this, and can be defined non-perturbatively in almost arbitrary spacetimes. Some quite general results are already known, in terms of dAobserver/d\u3a9source, the cross-sectional area per unit solid angle of a null geodesic spray emitted from some source and subsequently detected by some observer. We shall reformulate these results in terms of a suitably normalized null geodesic affine parameter and the van Vleck determinant, \u394vV. The contribution due to the null geodesic affine parameter is effectively the inverse square law for luminosity, and the van Vleck determinant can be viewed as providing a measure of deviations from the inverse square law. This formulation is closely related to the so-called Jacobi determinant, but the van Vleck determinant has somewhat nicer analytic properties and wider and deeper theoretical base in the general relativity, quantum physics, and quantum field theory communities. In the current article we shall concentrate on non-perturbative results, leaving near-FLRW perturbative investigation for future work

Stable gravastars with generalised exteriors

New spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti--de Sitter or de Sitter interior and a Schwarzschild--(anti)--de Sitter or Reissner--Nordstr\"{o}m exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviours of the equation of state for these parameters.Comment: 14 pages, 11 figures, to appear in Classical and Quantum Gravit