232 research outputs found
Brane-world Cosmologies with non-local bulk effects
It is very common to ignore the non-local bulk effects in the study of
brane-world cosmologies using the brane-world approach. However, we shall
illustrate through the use of three different scenarios, that the non-local
bulk-effect does indeed have significant impact on both the
initial and future behaviour of brane-world cosmologies.Comment: 17 pages, no figures, iopart.cls, submitted to CQ
Symmetries of Bianchi I space-times
All diagonal proper Bianchi I space-times are determined which admit certain
important symmetries. It is shown that for Homotheties, Conformal motions and
Kinematic Self-Similarities the resulting space-times are defined explicitly in
terms of a set of parameters whereas Affine Collineations, Ricci Collineations
and Curvature Collineations, if they are admitted, they determine the metric
modulo certain algebraic conditions. In all cases the symmetry vectors are
explicitly computed. The physical and the geometrical consequences of the
results are discussed and a new anisitropic fluid, physically valid solution
which admits a proper conformal Killing vector, is given.Comment: 19 pages, LaTex, Accepted for publication in Journal of Mathematical
Physic
Isotropic singularity in inhomogeneous brane cosmological models
We discuss the asymptotic dynamical evolution of spatially inhomogeneous
brane-world cosmological models close to the initial singularity. By
introducing suitable scale-invariant dependent variables and a suitable gauge,
we write the evolution equations of the spatially inhomogeneous brane
cosmological models with one spatial degree of freedom as a system of
autonomous first-order partial differential equations. We study the system
numerically, and we find that there always exists an initial singularity, which
is characterized by the fact that spatial derivatives are dynamically
negligible. More importantly, from the numerical analysis we conclude that
there is an initial isotropic singularity in all of these spatially
inhomogeneous brane cosmologies for a range of parameter values which include
the physically important cases of radiation and a scalar field source. The
numerical results are supported by a qualitative dynamical analysis and a
calculation of the past asymptotic decay rates. Although the analysis is local
in nature, the numerics indicates that the singularity is isotropic for all
relevant initial conditions. Therefore this analysis, and a preliminary
investigation of general inhomogeneous () models, indicates that it is
plausible that the initial singularity is isotropic in spatially inhomogeneous
brane-world cosmological models and consequently that brane cosmology naturally
gives rise to a set of initial data that provide the conditions for inflation
to subsequently take place.Comment: 32 pages with 8 pictures. submitted to Class. Quant. Gra
String-inspired cosmology: Late time transition from scaling matter era to dark energy universe caused by a Gauss-Bonnet coupling
The Gauss-Bonnet (GB) curvature invariant coupled to a scalar field
can lead to an exit from a scaling matter-dominated epoch to a late-time
accelerated expansion, which is attractive to alleviate the coincident problem
of dark energy. We derive the condition for the existence of cosmological
scaling solutions in the presence of the GB coupling for a general scalar-field
Lagrangian density , where is a kinematic
term of the scalar field. The GB coupling and the Lagrangian density are
restricted to be in the form and , respectively, where is a constant and is an
arbitrary function. We also derive fixed points for such a scaling Lagrangian
with a GB coupling and clarify the conditions
under which the scaling matter era is followed by a de-Sitter solution which
can appear in the presence of the GB coupling. Among scaling models proposed in
the current literature, we find that the models which allow such a cosmological
evolution are an ordinary scalar field with an exponential potential and a
tachyon field with an inverse square potential, although the latter requires a
coupling between dark energy and dark matter.Comment: 18 pages, 4 figures, version to appear in JCA
Scaling solutions from interacting fluids
We examine the dynamical implications of an interaction between some of the
fluid components of the universe. We consider the combination of three matter
components, one of which is a perfect fluid and the other two are interacting.
The interaction term generalizes the cases found in scalar field cosmologies
with an exponential potential. We find that attracting scaling solutions are
obtained in several regions of parameter space, that oscillating behaviour is
possible, and that new curvature scaling solutions exist. We also discuss the
inflationary behaviour of the solutions and present some of the constraints on
the strength of the coupling, namely those arising from nucleosynthesis.Comment: RevTeX, 21 pages, 8 figure
On the Asymptotic Behaviour of Cosmological Models in Scalar-Tensor Theories of Gravity
We study the qualitative properties of cosmological models in scalar-tensor
theories of gravity by exploiting the formal equivalence of these theories with
general relativity minimally coupled to a scalar field under a conformal
transformation and field redefinition. In particular, we investigate the
asymptotic behaviour of spatially homogeneous cosmological models in a class of
scalar-tensor theories which are conformally equivalent to general relativistic
Bianchi cosmologies with a scalar field and an exponential potential whose
qualitative features have been studied previously. Particular attention is
focussed on those scalar-tensor theory cosmological models, which are shown to
be self-similar, that correspond to general relativistic models that play an
important r\^{o}le in describing the asymptotic behaviour of more general
models (e.g., those cosmological models that act as early-time and late-time
attractors).Comment: 22 pages, submitted to Phys Rev
Self-Similarity in General Relativity \endtitle
The different kinds of self-similarity in general relativity are discussed,
with special emphasis on similarity of the ``first'' kind, corresponding to
spacetimes admitting a homothetic vector. We then survey the various classes of
self-similar solutions to Einstein's field equations and the different
mathematical approaches used in studying them. We focus mainly on spatially
homogenous and spherically symmetric self-similar solutions, emphasizing their
possible roles as asymptotic states for more general models. Perfect fluid
spherically symmetric similarity solutions have recently been completely
classified, and we discuss various astrophysical and cosmological applications
of such solutions. Finally we consider more general types of self-similar
models.Comment: TeX document, 53 page
Modified gravity in a viscous and non-isotropic background
We study the dynamical evolution of an model of gravity in a viscous
and anisotropic background which is given by a Bianchi type-I model of the
Universe. We find viable forms of gravity in which one is exactly the
Einsteinian model of gravity with a cosmological constant and other two are
power law models. We show that these two power law models are stable
with a suitable choice of parameters. We also examine three potentials which
exhibit the potential effect of models in the context of scalar tensor
theory. By solving different aspects of the model and finding the physical
quantities in the Jordan frame, we show that the equation of state parameter
satisfy the dominant energy condition. At last we show that the two power law
models behave like quintessence model at late times and also the shear
coefficient viscosity tends to zero at late times.Comment: 7 pages, 2 figure
Cosmology with exponential potentials
We examine in the context of general relativity the dynamics of a spatially
flat Robertson-Walker universe filled with a classical minimally coupled scalar
field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic
matter. This system is reduced to a first-order ordinary differential equation,
providing direct evidence on the acceleration/deceleration properties of the
system. As a consequence, for positive potentials, passage into acceleration
not at late times is generically a feature of the system, even when the
late-times attractors are decelerating. Furthermore, the structure formation
bound, together with the constraints on the present values of \Omega_{m},
w_{\phi} provide, independently of initial conditions and other parameters,
necessary conditions on \mu. Special solutions are found to possess intervals
of acceleration. For the almost cosmological constant case w_{\phi} ~ -1, as
well as, for the generic late-times evolution, the general relation
\Omega_{\phi}(w_{\phi}) is obtained.Comment: RevTex4, 9 pages, 2 figures, References adde
Coupled dark energy: Towards a general description of the dynamics
In dark energy models of scalar-field coupled to a barotropic perfect fluid,
the existence of cosmological scaling solutions restricts the Lagrangian of the
field \vp to p=X g(Xe^{\lambda \vp}), where X=-g^{\mu\nu} \partial_\mu \vp
\partial_\nu \vp /2, is a constant and is an arbitrary function.
We derive general evolution equations in an autonomous form for this Lagrangian
and investigate the stability of fixed points for several different dark energy
models--(i) ordinary (phantom) field, (ii) dilatonic ghost condensate, and
(iii) (phantom) tachyon. We find the existence of scalar-field dominant fixed
points (\Omega_\vp=1) with an accelerated expansion in all models
irrespective of the presence of the coupling between dark energy and dark
matter. These fixed points are always classically stable for a phantom field,
implying that the universe is eventually dominated by the energy density of a
scalar field if phantom is responsible for dark energy. When the equation of
state w_\vp for the field \vp is larger than -1, we find that scaling
solutions are stable if the scalar-field dominant solution is unstable, and
vice versa. Therefore in this case the final attractor is either a scaling
solution with constant \Omega_\vp satisfying 0<\Omega_\vp<1 or a
scalar-field dominant solution with \Omega_\vp=1.Comment: 21 pages, 5 figures; minor clarifications added, typos corrected and
references updated; final version to appear in JCA
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