23 research outputs found
Dynamical study of the empty Bianchi type I model in generalised scalar-tensor theory
A dynamical study of the generalised scalar-tensor theory in the empty
Bianchi type I model is made. We use a method from which we derive the sign of
the first and second derivatives of the metric functions and examine three
different theories that can all tend towards relativistic behaviours at late
time. We determine conditions so that the dynamic be in expansion and
decelerated at late time.Comment: 18 pages, 3 figures, to appear in General Relativity and Gravitatio
Patching up the No-Boundary Proposal with virtual Euclidean wormholes
In quantum cosmology, one often considers tunneling phenomena which may have
occurred in the early universe. Processes requiring quantum penetration of a
potential barrier include black hole pair creation and the decay of vacuum
domain walls. Ideally, one calculates the rates for such processes by finding
an instanton, or Euclidean solution of the field equations, which interpolates
between the initial and final states. In practice, however, it has become
customary to calculate such amplitudes using the No-Boundary Proposal of Hartle
and Hawking. A criticism of this method is that it does not use a single path
which interpolates between the initial and final states, but two disjoint
instantons: One divides the probability to create the final state from nothing
by the probability to create the initial state from nothing and decrees the
answer to be the rate of tunneling from the initial to the final state. Here,
we demonstrate the validity of this approach by constructing continuous paths
connecting the ingoing and outgoing data, which may be viewed as perturbations
of the set of disconnected instantons. They are off-shell, but will still
dominate the path integral as they have action arbitrarily close to the
no-boundary action. In this picture, a virtual domain wall, or wormhole, is
created and annihilated in such a way as to interface between the disjoint
instantons. Decay rates calculated using our construction differ from decay
rates calculated using the No-Boundary Proposal only in the prefactor; the
exponent, which usually dominates the result, remains unchanged.Comment: 23 pages REVTeX plus 7 figure
Quantum Decay of Domain Walls in Cosmology II: Hamiltonian Approach
This paper studies the decay of a large, closed domain wall in a closed
universe. Such walls can form in the presence of a broken, discrete symmetry.
We study a novel process of quantum decay for such a wall, in which the vacuum
fluctuates from one discrete state to another throughout one half of the
universe, so that the wall decays into pure field energy. Equivalently, the
fluctuation can be thought of as the nucleation of a second closed domain wall
of zero size, followed by its growth by quantum tunnelling and its collision
with the first wall, annihilating both. We therefore study the 2-wall system
coupled to a spherically symmetric gravitational field. We derive a simple form
of the 2-wall action, use Dirac quantization, obtain the 2-wall wave function
for annihilation, find from it the barrier factor for this quantum tunneling,
and thereby get the decay probability. This is the second paper of a series.Comment: 27 pages LaTeX, using revtex and psfig. 3 figure
Density Perturbations in the Brans-Dicke Theory
We analyse the fate of density perturbation in the Brans-Dicke Theory, giving
a general classification of the solutions of the perturbed equations when the
scale factor of the background evolves as a power law. We study with details
the cases of vacuum, inflation, radiation and incoherent matter. We find, for
the a negative Brans-Dicke parameter, a significant amplification of
perturbations.Comment: 26 pages, latex fil
Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric
In this work, we have consider Kaluza-Klein Cosmology for anisotropic
universe where the universe is filled with variable modified chaplygin gas
(VMCG). Here we find normal scalar field and the self interacting
potential to describe the VMCG Cosmology. Also we graphically
analyzed the geometrical parameters named {\it statefinder parameters} in
anisotropic Kaluza-Klein model. Next, we consider a Kaluza-Klein model of
interacting VMCG with dark matter in the Einstein gravity framework. Here we
construct the three dimensional autonomous dynamical system of equations for
this interacting model with the assumption that the dark energy and the dark
matter are interact between them and for that we also choose the interaction
term. We convert that interaction terms to its dimensionless form and perform
stability analysis and solve them numerically. We obtain a stable scaling
solution of the equations in Kaluza-Klein model and graphically represent
solutions.Comment: 11 pages, 13 figure
Solution generating in scalar-tensor theories with a massless scalar field and stiff perfect fluid as a source
We present a method for generating solutions in some scalar-tensor theories
with a minimally coupled massless scalar field or irrotational stiff perfect
fluid as a source. The method is based on the group of symmetries of the
dilaton-matter sector in the Einstein frame. In the case of Barker's theory the
dilaton-matter sector possesses SU(2) group of symmetries. In the case of
Brans-Dicke and the theory with "conformal coupling", the dilaton- matter
sector has as a group of symmetries. We describe an explicit
algorithm for generating exact scalar-tensor solutions from solutions of
Einstein-minimally-coupled-scalar-field equations by employing the nonlinear
action of the symmetry group of the dilaton-matter sector. In the general case,
when the Einstein frame dilaton-matter sector may not possess nontrivial
symmetries we also present a solution generating technique which allows us to
construct exact scalar-tensor solutions starting with the solutions of
Einstein-minimally-coupled-scalar-field equations. As an illustration of the
general techniques, examples of explicit exact solutions are constructed. In
particular, we construct inhomogeneous cosmological scalar-tensor solutions
whose curvature invariants are everywhere regular in space-time. A
generalization of the method for scalar-tensor-Maxwell gravity is outlined.Comment: 10 pages,Revtex; v2 extended version, new parts added and some parts
rewritten, results presented more concisely, some simple examples of
homogeneous solutions replaced with new regular inhomogeneous solutions,
typos corrected, references and acknowledgements added, accepted for
publication in Phys.Rev.
Scalar-Tensor Cosmological Models
We analyze the qualitative behaviors of scalar-tensor cosmologies with an
arbitrary monotonic function. In particular, we are interested
on scalar-tensor theories distinguishable at early epochs from General
Relativity (GR) but leading to predictions compatible with solar-system
experiments. After extending the method developed by Lorentz-Petzold and
Barrow, we establish the conditions required for convergence towards GR at
. Then, we obtain all the asymptotic analytical solutions
at early times which are possible in the framework of these theories. The
subsequent qualitative evolution, from these asymptotic solutions until their
later convergence towards GR, has been then analyzed by means of numerical
computations. From this analysis, we have been able to establish a
classification of the different qualitative behaviors of scalar-tensor
cosmological models with an arbitrary monotonic function.Comment: uuencoded compressed postscript file containing 41 pages, with 9
figures, accepted for publication in Physical Review
Self-similar cosmological solutions with a non-minimally coupled scalar field
We present self-similar cosmological solutions for a barotropic fluid plus
scalar field with Brans-Dicke-type coupling to the spacetime curvature and an
arbitrary power-law potential energy. We identify all the fixed points in the
autonomous phase-plane, including a scaling solution where the fluid density
scales with the scalar field's kinetic and potential energy. This is related by
a conformal transformation to a scaling solution for a scalar field with
exponential potential minimally coupled to the spacetime curvature, but
non-minimally coupled to the barotropic fluid. Radiation is automatically
decoupled from the scalar field, but energy transfer between the field and
non-relativistic dark matter can lead to a change to an accelerated expansion
at late times in the Einstein frame. The scalar field density can mimic a
cosmological constant even for steep potentials in the strong coupling limit.Comment: 10 pages, 1 figure, revtex version to appear in Phys Rev D,
references adde
Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
We perform a Hamiltonian reduction of spherically symmetric Einstein gravity
with a thin dust shell of positive rest mass. Three spatial topologies are
considered: Euclidean (R^3), Kruskal (S^2 x R), and the spatial topology of a
diametrically identified Kruskal (RP^3 - {a point at infinity}). For the
Kruskal and RP^3 topologies the reduced phase space is four-dimensional, with
one canonical pair associated with the shell and the other with the geometry;
the latter pair disappears if one prescribes the value of the Schwarzschild
mass at an asymptopia or at a throat. For the Euclidean topology the reduced
phase space is necessarily two-dimensional, with only the canonical pair
associated with the shell surviving. A time-reparametrization on a
two-dimensional phase space is introduced and used to bring the shell
Hamiltonians to a simpler (and known) form associated with the proper time of
the shell. An alternative reparametrization yields a square-root Hamiltonian
that generalizes the Hamiltonian of a test shell in Minkowski space with
respect to Minkowski time. Quantization is briefly discussed. The discrete mass
spectrum that characterizes natural minisuperspace quantizations of vacuum
wormholes and RP^3-geons appears to persist as the geometrical part of the mass
spectrum when the additional matter degree of freedom is added.Comment: 36 pages, REVTeX v3.1 with amsfonts. (References updated; minor typos
corrected.