1,954 research outputs found
Vector and tensor perturbations in Horava-Lifshitz cosmology
We study cosmological vector and tensor perturbations in Horava-Lifshitz
gravity, adopting the most general Sotiriou-Visser-Weinfurtner generalization
without the detailed balance but with projectability condition. After deriving
the general formulas in a flat FRW background, we find that the vector
perturbations are identical to those given in general relativity. This is true
also in the non-flat cases. For the tensor perturbations, high order
derivatives of the curvatures produce effectively an anisotropic stress, which
could have significant efforts on the high-frequency modes of gravitational
waves, while for the low-frenquency modes, the efforts are negligible. The
power spectrum is scale-invariant in the UV regime, because of the particular
dispersion relations. But, due to lower-order corrections, it will eventually
reduce to that given in GR in the IR limit. Applying the general formulas to
the de Sitter and power-law backgrounds, we calculate the power spectrum and
index, using the uniform approximations, and obtain their analytical
expressions in both cases.Comment: Correct some typos and add new references. Version to be published in
Physical Reviews
Relativistic Weierstrass random walks
The Weierstrass random walk is a paradigmatic Markov chain giving rise to a
L\'evy-type superdiffusive behavior. It is well known that Special Relativity
prevents the arbitrarily high velocities necessary to establish a
superdiffusive behavior in any process occurring in Minkowski spacetime,
implying, in particular, that any relativistic Markov chain describing
spacetime phenomena must be essentially Gaussian. Here, we introduce a simple
relativistic extension of the Weierstrass random walk and show that there must
exist a transition time delimiting two qualitative distinct dynamical
regimes: the (non-relativistic) superdiffusive L\'evy flights, for ,
and the usual (relativistic) Gaussian diffusion, for . Implications of
this crossover between different diffusion regimes are discussed for some
explicit examples. The study of such an explicit and simple Markov chain can
shed some light on several results obtained in much more involved contexts.Comment: 5 pages, final version to appear in PR
Response of a particle in a one-dimensional lattice to an applied force: Dynamics of the effective mass
We study the behaviour of the expectation value of the acceleration of a
particle in a one-dimensional periodic potential when an external homogeneous
force is suddenly applied. The theory is formulated in terms of modified Bloch
states that include the interband mixing induced by the force. This approach
allows us to understand the behaviour of the wavepacket, which responds with a
mass that is initially the bare mass, and subsequently oscillates around the
value predicted by the effective mass. If Zener tunneling can be neglected, the
expression obtained for the acceleration of the particle is valid over
timescales of the order of a Bloch oscillation, which are of interest for
experiments with cold atoms in optical lattices. We discuss how these
oscillations can be tuned in an optical lattice for experimental detection.Comment: 15 pages, 12 figure
Cosmological predictions from the Misner brane
Within the spirit of five-dimensional gravity in the Randall-Sundrum
scenario, in this paper we consider cosmological and gravitational implications
induced by forcing the spacetime metric to satisfy a Misner-like symmetry. We
first show that in the resulting Misner-brane framework the Friedmann metric
for a radiation dominated flat universe and the Schwarzschild or anti-de Sitter
black holes metrics are exact solutions on the branes, but the model cannot
accommodate any inflationary solution. The horizon and flatness problems can
however be solved in Misner-brane cosmology by causal and noncausal
communications through the extra dimension between distant regions which are
outside the horizon. Based on a semiclassical approximation to the
path-integral approach, we have calculated the quantum state of the
Misner-brane universe and the quantum perturbations induced on its metric by
brane propagation along the fifth direction. We have then considered testable
predictions from our model. These include a scale-invariant spectrum of density
perturbations whose amplitude can be naturally accommodated to the required
value 10, and a power spectrum of CMB anisotropies whose
acoustic peaks are at the same sky angles as those predicted by inflationary
models, but having much smaller secondary-peak intensities. These predictions
seem to be compatible with COBE and recent Boomerang and Maxima measurementsComment: 16 pages, RevTe
Thermal effects on slow-roll dynamics
A description of the transition from the inflationary epoch to radiation
domination requires the understanding of quantum fields out of thermal
equilibrium, particle creation and thermalisation. This can be studied from
first principles by solving a set of truncated real-time Schwinger-Dyson
equations, written in terms of the mean field (inflaton) and the field
propagators, derived from the two-particle irreducible effective action. We
investigate some aspects of this problem by considering the dynamics of a
slow-rolling mean field coupled to a second quantum field, using a \phi^2\chi^2
interaction. We focus on thermal effects. It is found that interactions lead to
an earlier end of slow-roll and that the evolution afterwards depends on
details of the heatbath.Comment: 25 pages, 11 eps figures. v2: paper reorganized, title changed,
conclusions unchanged, to appear in PR
Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions
Noninteracting fermions, placed in a system with a continuous density of
states, may have zeros in the -fermion canonical partition function on the
positive real axis (or very close to it), even for a small number of
particles. This results in a singular free energy, and instability in other
thermal properties of the system. In the context of trapped fermions in a
harmonic oscillator, these zeros are shown to be unphysical. By contrast,
similar bosonic calculations with continuous density of states yield sensible
results.Noninteracting fermions, placed in a system with a continuous density
of states yield sensible results.Comment: 5 pages and 5 figure
Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
We examine the motion in Schwarzschild spacetime of a point particle endowed
with a scalar charge. The particle produces a retarded scalar field which
interacts with the particle and influences its motion via the action of a
self-force. We exploit the spherical symmetry of the Schwarzschild spacetime
and decompose the scalar field in spherical-harmonic modes. Although each mode
is bounded at the position of the particle, a mode-sum evaluation of the
self-force requires regularization because the sum does not converge: the
retarded field is infinite at the position of the particle. The regularization
procedure involves the computation of regularization parameters, which are
obtained from a mode decomposition of the Detweiler-Whiting singular field;
these are subtracted from the modes of the retarded field, and the result is a
mode-sum that converges to the actual self-force. We present such a computation
in this paper. There are two main aspects of our work that are new. First, we
define the regularization parameters as scalar quantities by referring them to
a tetrad decomposition of the singular field. Second, we calculate four sets of
regularization parameters (denoted schematically by A, B, C, and D) instead of
the usual three (A, B, and C). As proof of principle that our methods are
reliable, we calculate the self-force acting on a scalar charge in circular
motion around a Schwarzschild black hole, and compare our answers with those
recorded in the literature.Comment: 38 pages, 2 figure
Critical behavior of Born Infeld AdS black holes in higher dimensions
Based on a canonical framework, we investigate the critical behavior of
Born-Infeld AdS black holes in higher dimensions. As a special case,
considering the appropriate limit, we also analyze the critical phenomena for
Reissner Nordstrom AdS black holes. The critical points are marked by the
divergences in the heat capacity at constant charge. The static critical
exponents associated with various thermodynamic entities are computed and shown
to satisfy the thermodynamic scaling laws. These scaling laws have also been
found to be compatible with the static scaling hypothesis. Furthermore, we show
that the values of these exponents are universal and do not depend on the
spatial dimensionality of the AdS space. We also provide a suggestive way to
calculate the critical exponents associated with the spatial correlation which
satisfy the scaling laws of second kind.Comment: LaTex, 22 pages, 12 figures, minor modifications in text, To appear
in Phys. Rev.
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