2,820 research outputs found
Boltzmann hierarchy for the cosmic microwave background at second order including photon polarization
Non-gaussianity and B-mode polarization are particularly interesting features
of the cosmic microwave background, as -- at least in the standard model of
cosmology -- their only sources to first order in cosmological perturbation
theory are primordial, possibly generated during inflation. If the primordial
sources are small, the question arises how large is the non-gaussianity and
B-mode background induced in second-order from the initially gaussian and
scalar perturbations. In this paper we derive the Boltzmann hierarchy for the
microwave background photon phase-space distributions at second order in
cosmological perturbation theory including the complete polarization
information, providing the basis for further numerical studies. As an aside we
note that the second-order collision term contains new sources of B-mode
polarization and that no polarization persists in the tight-coupling limit.Comment: LaTeX, 33 page
Integration over connections in the discretized gravitational functional integrals
The result of performing integrations over connection type variables in the
path integral for the discrete field theory may be poorly defined in the case
of non-compact gauge group with the Haar measure exponentially growing in some
directions. This point is studied in the case of the discrete form of the first
order formulation of the Einstein gravity theory. Here the result of interest
can be defined as generalized function (of the rest of variables of the type of
tetrad or elementary areas) i. e. a functional on a set of probe functions. To
define this functional, we calculate its values on the products of components
of the area tensors, the so-called moments. The resulting distribution (in
fact, probability distribution) has singular (-function-like) part with
support in the nonphysical region of the complex plane of area tensors and
regular part (usual function) which decays exponentially at large areas. As we
discuss, this also provides suppression of large edge lengths which is
important for internal consistency, if one asks whether gravity on short
distances can be discrete. Some another features of the obtained probability
distribution including occurrence of the local maxima at a number of the
approximately equidistant values of area are also considered.Comment: 22 page
Spherical Harmonic Decomposition on a Cubic Grid
A method is described by which a function defined on a cubic grid (as from a
finite difference solution of a partial differential equation) can be resolved
into spherical harmonic components at some fixed radius. This has applications
to the treatment of boundary conditions imposed at radii larger than the size
of the grid, following Abrahams, Rezzola, Rupright et al.(gr-qc/9709082}. In
the method described here, the interpolation of the grid data to the
integration 2-sphere is combined in the same step as the integrations to
extract the spherical harmonic amplitudes, which become sums over grid points.
Coordinates adapted to the integration sphere are not needed.Comment: 5 pages, LaTeX uses cjour.cls (supplied
Response of the common mode of interferometric detectors to a stochastic background of massive scalar radiation
We compute the angular pattern and the overlap reduction functions for the
geodesic and non-geodesic response of the common mode of two interferometers
interacting with a stochastic, massive scalar background. We also discuss the
possible overlap between common and differential modes. We find that the
cross-correlated response of two common modes to a non-relativistic background
may be higher than the response of two differential modes to the same
background.Comment: 8 pages, 4 figures, revte
About the Statistical Properties of Cosmological Billiards
We summarize some recent progress in the understanding of the statistical
properties of cosmological billiards.Comment: 10 pages, 5 figures, 2 tables, Proceedings of The second
Galileo-XuGuangqi Meeting, 11-16/07/2010, Ventimiglia, Ital
Higgs Mechanism for Gravitons
Just like the vector gauge bosons in the gauge theories, it is now known that
gravitons acquire mass in the process of spontaneous symmetry breaking of
diffeomorphisms through the condensation of scalar fields. The point is that we
should find the gravitational Higgs mechanism such that it results in massive
gravity in a flat Minkowski space-time without non-unitary propagating modes.
This is usually achieved by including higher-derivative terms in scalars and
tuning the cosmological constant to be a negative value in a proper way.
Recently, a similar but different gravitational Higgs mechanism has been
advocated by Chamseddine and Mukhanov where one can relax the negative
cosmological constant to zero or positive one. In this work, we investigate why
the non-unitary ghost mode decouples from physical Hilbert space in a general
space-time dimension. Moreover, we generalize the model to possess an arbitrary
potential and clarify under what conditions the general model exhibits the
gravitational Higgs mechanism. By searching for solutions to the conditions, we
arrive at two classes of potentials exhibiting gravitational Higgs mechanism.
One class includes the model by Chamseddine and Mukhanov in a specific case
while the other is completely a new model.Comment: 11 page
Limit to General Relativity in f(R) theories of gravity
We discuss two aspects of f(R) theories of gravity in metric formalism. We
first study the reasons to introduce a scalar-tensor representation for these
theories and the behavior of this representation in the limit to General
Relativity, f(R)--> R. We find that the scalar-tensor representation is well
behaved even in this limit. Then we work out the exact equations for
spherically symmetric sources using the original f(R) representation, solve the
linearized equations, and compare our results with recent calculations of the
literature. We observe that the linearized solutions are strongly affected by
the cosmic evolution, which makes very unlikely that the cosmic speedup be due
to f(R) models with correcting terms relevant at low curvatures.Comment: 8 pages; small changes to match published version (some comments,
references added, title corrected); to appear in Phys.Rev.
A stationary vacuum solution dual to the Kerr solution
We present a stationary axially symmetric two parameter vacuum solution which
could be considered as ``dual'' to the Kerr solution. It is obtained by
removing the mass parameter from the function of the radial coordinate and
introducing a dimensionless parameter in the function of the angle coordinate
in the metric functions. It turns out that it is in fact the massless limit of
the Kerr - NUT solution.Comment: Latex, 4 pages, minor modifications in title and discussion. Accepted
in Mod. Phys. Lett.
Quantum Interference to Measure Spacetime Curvature: A Proposed Experiment at the Intersection of Quantum Mechanics and General Relativity
An experiment in Low Earth Orbit (LEO) is proposed to measure components of
the Riemann curvature tensor using atom interferometry. We show that the
difference in the quantum phase of an atom that can travel along
two intersecting geodesics is given by times the spacetime
volume contained within the geodesics. Our expression for also
holds for gravitational waves in the long wavelength limit.Comment: 7 pages LaTeXed with RevTeX 4.0, 2 figures. Submitted to the 2003
Gravity Research Foundation Essay Contes
Verifying black hole orbits with gravitational spectroscopy
Gravitational waves from test masses bound to geodesic orbits of rotating
black holes are simulated, using Teukolsky's black hole perturbation formalism,
for about ten thousand generic orbital configurations. Each binary radiates
power exclusively in modes with frequencies that are
integer-linear-combinations of the orbit's three fundamental frequencies. The
following general spectral properties are found with a survey of orbits: (i)
99% of the radiated power is typically carried by a few hundred modes, and at
most by about a thousand modes, (ii) the dominant frequencies can be grouped
into a small number of families defined by fixing two of the three integer
frequency multipliers, and (iii) the specifics of these trends can be
qualitatively inferred from the geometry of the orbit under consideration.
Detections using triperiodic analytic templates modeled on these general
properties would constitute a verification of radiation from an adiabatic
sequence of black hole orbits and would recover the evolution of the
fundamental orbital frequencies. In an analogy with ordinary spectroscopy, this
would compare to observing the Bohr model's atomic hydrogen spectrum without
being able to rule out alternative atomic theories or nuclei. The suitability
of such a detection technique is demonstrated using snapshots computed at
12-hour intervals throughout the last three years before merger of a kludged
inspiral. Because of circularization, the number of excited modes decreases as
the binary evolves. A hypothetical detection algorithm that tracks mode
families dominating the first 12 hours of the inspiral would capture 98% of the
total power over the remaining three years.Comment: 18 pages, expanded section on detection algorithms and made minor
edits. Final published versio
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