12 research outputs found
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
Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology
Cosmography is the part of cosmology that proceeds by making minimal dynamic assumptions.
That is, one does not assume the Friedmann equations (Einstein equations) unless and until absolutely necessary. On the other hand, cosmodynamics is the part of cosmology that relates the geometry to the density and pressure using the Friedmann equations. In both frameworks, we consider the amount of information and the nature of the constraints we can obtain from the Hubble flow in a FLRW universe. Indeed, the cosmological parameters contained in the Hubble relation between distance and redshift provide information on the behaviour of the universe (expansion, acceleration etc...). In the first framework, it is possible to concentrate more directly on the observational situation in a model-independent manner. We perform a number of inter-related cosmographic fits to supernova datasets, and pay particular attention to the extent to which the choice of distance scale and manner of representing the redshift scale affect the cosmological parameters. In the second framework, we use the class of w-parameter models which has become increasingly popular in the last decade. We explore the extent to which a constraint on the w-parameter leads to useful and non-trivial constraints on the Hubble flow in terms of cosmological parameters H(z), density p(z), density parameter O(z), distance scales d(z), and lookback time T(z). On another front, Numerical Relativity has experienced many breakthroughs since 2005, with full inspiral-merger-ringdown simulations now possible. One of the main goals is to provide very accurate templates of gravitational waves for ground-based and space-based interferometers. We explore the potential of a very recent and accurate numerical method, the Spectral Element Method (SEM), for Numerical Relativity, by treating a singular Schwarszchild black hole evolution as a test case. Spectral elements combine the theory of spectral and pseudo-spectral methods for high order polynomials and the variational formulation of finite elements and the associated geometric flexibility. We use the BSSN formulation of the Einstein equations with the method of the moving punctures. After applying the variational formulation to the BSSN system, we present several possible weak forms of this system and its spectral element discretization in space. We use a Runge-Kutta fourth order time discretization. The accuracy of high order methods can deteriorate in the presence of discontinuities or sharp gradients. We show that we can treat the element that contains the puncture with a filtering method to avoid artificial and spurious oscillations. These might form and propagate into the domain coming from discontinuous initial data from the BSSN system
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
Gravastars must have anisotropic pressures
One of the very small number of serious alternatives to the usual concept of
an astrophysical black hole is the "gravastar" model developed by Mazur and
Mottola; and a related phase-transition model due to Laughlin et al. We
consider a generalized class of similar models that exhibit continuous pressure
-- without the presence of infinitesimally thin shells. By considering the
usual TOV equation for static solutions with negative central pressure, we find
that gravastars cannot be perfect fluids -- anisotropic pressures in the
"crust" of a gravastar-like object are unavoidable. The anisotropic TOV
equation can then be used to bound the pressure anisotropy. The transverse
stresses that support a gravastar permit a higher compactness than is given by
the Buchdahl--Bondi bound for perfect fluid stars. Finally we comment on the
qualitative features of the equation of state that gravastar material must have
if it is to do the desired job of preventing horizon formation.Comment: V1: 15 pages; 4 figures; uses iopart.cls; V2: 16 pages; added 3
references and brief discussio
Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology
Cosmography is the part of cosmology that proceeds by making minimal dynamic assumptions.
That is, one does not assume the Friedmann equations (Einstein equations) unless and until absolutely necessary. On the other hand, cosmodynamics is the part of cosmology that relates the geometry to the density and pressure using the Friedmann equations. In both frameworks, we consider the amount of information and the nature of the constraints we can obtain from the Hubble flow in a FLRW universe. Indeed, the cosmological parameters contained in the Hubble relation between distance and redshift provide information on the behaviour of the universe (expansion, acceleration etc...). In the first framework, it is possible to concentrate more directly on the observational situation in a model-independent manner. We perform a number of inter-related cosmographic fits to supernova datasets, and pay particular attention to the extent to which the choice of distance scale and manner of representing the redshift scale affect the cosmological parameters. In the second framework, we use the class of w-parameter models which has become increasingly popular in the last decade. We explore the extent to which a constraint on the w-parameter leads to useful and non-trivial constraints on the Hubble flow in terms of cosmological parameters H(z), density p(z), density parameter O(z), distance scales d(z), and lookback time T(z). On another front, Numerical Relativity has experienced many breakthroughs since 2005, with full inspiral-merger-ringdown simulations now possible. One of the main goals is to provide very accurate templates of gravitational waves for ground-based and space-based interferometers. We explore the potential of a very recent and accurate numerical method, the Spectral Element Method (SEM), for Numerical Relativity, by treating a singular Schwarszchild black hole evolution as a test case. Spectral elements combine the theory of spectral and pseudo-spectral methods for high order polynomials and the variational formulation of finite elements and the associated geometric flexibility. We use the BSSN formulation of the Einstein equations with the method of the moving punctures. After applying the variational formulation to the BSSN system, we present several possible weak forms of this system and its spectral element discretization in space. We use a Runge-Kutta fourth order time discretization. The accuracy of high order methods can deteriorate in the presence of discontinuities or sharp gradients. We show that we can treat the element that contains the puncture with a filtering method to avoid artificial and spurious oscillations. These might form and propagate into the domain coming from discontinuous initial data from the BSSN system