Cosmographic analysis of dark energy

The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a FLRW spacetime, but does not intrinsically make any dynamical assumptions. This suggests that it should be possible to estimate the parameters defining the Hubble relation without making any dynamical assumptions. To test this idea, we perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets, paying careful attention to the systematic uncertainties. Based on this supernova data, the "preponderance of evidence" certainly suggests an accelerating universe. However we would argue that (unless one uses additional dynamical and observational information, and makes additional theoretical assumptions) this conclusion is not currently supported "beyond reasonable doubt". As part of the analysis we develop two particularly transparent graphical representations of the redshift-distance relation -- representations in which acceleration versus deceleration reduces to the question of whether the relevant graph slopes up or down.Comment: 14 pages. To appear in the Proceedings of DARK 2009 -- The Seventh International Heidelberg Conference on Dark Matter in Astro and Particle Physics, Christchurch, New Zealand, January 200

Cosmological milestones and gravastars - topics in general relativity

In this thesis, we consider two different problems relevant to general relativity. Over the last few years, opinions on physically relevant singularities occurring in FRW cosmologies have considerably changed. We present an extensive catalogue of such cosmological milestones using generalized power series both at the kinematical and dynamical level. We define the notion of "scale factor singularity" and explore its relation to polynomial and differential curvature singularities. We also extract dynamical information using the Friedmann equations and derive necessary and sufficient conditions for the existence of cosmological milestones such as big bangs, big crunches, big rips, sudden singularities and extremality events. Specifically, we provide a complete characterization of cosmological milestones for which the dominant energy condition is satisfied. The second problem looks at one of the very small number of serious alternatives to the usual concept of an astrophysical black hole, that is, the gravastar model developed by Mazur and Mottola. By considering a generalized class of similar models with continuous pressure (no infinitesimally thin shells) and negative central pressure, we demonstrate that gravastars cannot be perfect fluid spheres: anisotropic pressures are unavoidable. We provide bounds on the necessary anisotropic pressure and show that these transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl-Bondi bound for perfect fluid stars. We also comment on the qualitative features of the equation of state that such gravastar-like objects without any horizon must have.Comment: 171 pages; MSc thesi

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

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

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