4,664 research outputs found
Quantization of perturbations during inflation in the 1+3 covariant formalism
This note derives the analogue of the Mukhanov-Sasaki variables both for
scalar and tensor perturbations in the 1+3 covariant formalism. The possibility
of generalizing them to non-flat Friedmann-Lemaitre universes is discussed.Comment: 4 pages: v2 has minor changes to match published versio
General up to next-nearest neighbour elasticity of triangular lattices in three dimensions
We establish the most general form of the discrete elasticity of a 2D
triangular lattice embedded in three dimensions, taking into account up to
next-nearest neighbour interactions. Besides crystalline system, this is
relevant to biological physics (e.g., red blood cell cytoskeleton) and soft
matter (e.g., percolating gels, etc.). In order to correctly impose the
rotational invariance of the bulk terms, it turns out to be necessary to take
into account explicitly the elasticity associated with the vertices located at
the edges of the lattice. We find that some terms that were suspected in the
litterature to violate rotational symmetry are in fact admissibl
The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
This article presents the first computation of the complete bispectrum of the
cosmic microwave background temperature anisotropies arising from the evolution
of all cosmic fluids up to second order, including neutrinos. Gravitational
couplings, electron density fluctuations and the second order Boltzmann
equation are fully taken into account. Comparison to limiting cases that
appeared previously in the literature are provided. These are regimes for which
analytical insights can be given. The final results are expressed in terms of
equivalent fNL for different configurations. It is found that for moments up to
lmax=2000, the signal generated by non-linear effects is equivalent to fNL~5
for both local-type and equilateral-type primordial non-Gaussianity.Comment: 44 pages, 8 figure
Simulation of equatorial von Neumann measurements on GHZ states using nonlocal resources
Reproducing with elementary resources the correlations that arise when a
quantum system is measured (quantum state simulation), allows one to get
insight on the operational and computational power of quantum correlations. We
propose a family of models that can simulate von Neumann measurements in the
x-y plane of the Bloch sphere on n-partite GHZ states using only bipartite
nonlocal boxes. For the tripartite and fourpartite states, the models use only
bipartite nonlocal boxes; they can be translated into classical communication
schemes with finite average communication cost.Comment: 15 pages, 4 figures, published versio
CMB spectra and bispectra calculations: making the flat-sky approximation rigorous
This article constructs flat-sky approximations in a controlled way in the
context of the cosmic microwave background observations for the computation of
both spectra and bispectra. For angular spectra, it is explicitly shown that
there exists a whole family of flat-sky approximations of similar accuracy for
which the expression and amplitude of next to leading order terms can be
explicitly computed. It is noted that in this context two limiting cases can be
encountered for which the expressions can be further simplified. They
correspond to cases where either the sources are localized in a narrow region
(thin-shell approximation) or are slowly varying over a large distance (which
leads to the so-called Limber approximation). Applying this to the calculation
of the spectra it is shown that, as long as the late integrated Sachs-Wolfe
contribution is neglected, the flat-sky approximation at leading order is
accurate at 1% level for any multipole. Generalization of this construction
scheme to the bispectra led to the introduction of an alternative description
of the bispectra for which the flat-sky approximation is well controlled. This
is not the case for the usual description of the bispectrum in terms of reduced
bispectrum for which a flat-sky approximation is proposed but the
next-to-leading order terms of which remain obscure.Comment: 20 pages, 12 figure
Cosmic microwave background bispectrum on small angular scales
This article investigates the non-linear evolution of cosmological
perturbations on sub-Hubble scales in order to evaluate the unavoidable
deviations from Gaussianity that arise from the non-linear dynamics. It shows
that the dominant contribution to modes coupling in the cosmic microwave
background temperature anisotropies on small angular scales is driven by the
sub-Hubble non-linear evolution of the dark matter component. The perturbation
equations, involving in particular the first moments of the Boltzmann equation
for the photons, are integrated up to second order in perturbations. An
analytical analysis of the solutions gives a physical understanding of the
result as well as an estimation of its order of magnitude. This allows to
quantify the expected deviation from Gaussianity of the cosmic microwave
background temperature anisotropy and, in particular, to compute its bispectrum
on small angular scales. Restricting to equilateral configurations, we show
that the non-linear evolution accounts for a contribution that would be
equivalent to a constant primordial non-Gaussianity of order fNL~25 on scales
ranging approximately from l~1000 to l~3000.Comment: 21 pages, replaced to match published versio
The Role of Normalization in the Belief Propagation Algorithm
An important part of problems in statistical physics and computer science can
be expressed as the computation of marginal probabilities over a Markov Random
Field. The belief propagation algorithm, which is an exact procedure to compute
these marginals when the underlying graph is a tree, has gained its popularity
as an efficient way to approximate them in the more general case. In this
paper, we focus on an aspect of the algorithm that did not get that much
attention in the literature, which is the effect of the normalization of the
messages. We show in particular that, for a large class of normalization
strategies, it is possible to focus only on belief convergence. Following this,
we express the necessary and sufficient conditions for local stability of a
fixed point in terms of the graph structure and the beliefs values at the fixed
point. We also explicit some connexion between the normalization constants and
the underlying Bethe Free Energy
Anisotropy of the astrophysical gravitational wave background: analytic expression of the angular power spectrum and correlation with cosmological observations
Unresolved and resolved sources of gravitational waves are at the origin of a
stochastic gravitational wave background. While the computation of its mean
density as a function of frequency in a homogeneous and isotropic universe is
standard lore, the computation of its anisotropies requires to understand the
coarse graining from local systems, to galactic scales and then to cosmology.
An expression of the gravitational wave energy density valid in any general
spacetime is derived. It is then specialized to a perturbed
Friedmann-Lema\^itre spacetime in order to determine the angular power spectrum
of this stochastic background as well as its correlation with other
cosmological probes, such as the galaxy number counts and weak lensing. Our
result for the angular power spectrum also provides an expression for the
variance of the gravitational wave background.Comment: 22 pages, 2 figure
Local stability of Belief Propagation algorithm with multiple fixed points
A number of problems in statistical physics and computer science can be
expressed as the computation of marginal probabilities over a Markov random
field. Belief propagation, an iterative message-passing algorithm, computes
exactly such marginals when the underlying graph is a tree. But it has gained
its popularity as an efficient way to approximate them in the more general
case, even if it can exhibits multiple fixed points and is not guaranteed to
converge. In this paper, we express a new sufficient condition for local
stability of a belief propagation fixed point in terms of the graph structure
and the beliefs values at the fixed point. This gives credence to the usual
understanding that Belief Propagation performs better on sparse graphs.Comment: arXiv admin note: substantial text overlap with arXiv:1101.417
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