687 research outputs found
Polarization of the Microwave Background in Defect Models
We compute the polarization power spectra for global strings, monopoles,
textures and nontopological textures, and compare them to inflationary models.
We find that topological defect models predict a significant (1 microK)
contribution to magnetic type polarization on degree angular scales, which is
produced by the large vector component of the defect source. We also
investigate the effect of decoherence on polarization. It leads to a smoothing
of acoustic oscillations both in temperature and polarization power spectra and
strongly suppresses the cross-correlation between temperature and polarization
relative to inflationary models. Presence or absence of magnetic polarization
or cross-correlation would be a strong discriminator between the two theories
of structure formation and will be testable with the next generation of CMB
satellites.Comment: 4 pages, 3 figures, RevTeX fil
Lensing of the CMB: Non Gaussian aspects
We study the generation of CMB anisotropies by gravitational lensing on small
angular scales. We show these fluctuations are not Gaussian. We prove that the
power spectrum of the tail of the CMB anisotropies on small angular scales
directly gives the power spectrum of the deflection angle. We show that the
generated power on small scales is correlated with the large scale gradient.
The cross correlation between large scale gradient and small scale power can be
used to test the hypothesis that the extra power is indeed generated by
lensing. We compute the three and four point function of the temperature in the
small angle limit. We relate the non-Gaussian aspects presented in this paper
as well as those in our previous studies of the lensing effects on large scales
to the three and four point functions. We interpret the statistics proposed in
terms of different configurations of the four point function and show how they
relate to the statistic that maximizes the S/N.Comment: Changes to match accepted version in PRD, 20 pages 10 figures. Better
resolution images of the figures can be found at
http://www.sns.ias.edu/~matiasz/RESEARCH/cmblensing.htm
Constrained probability distributions of correlation functions
Context: Two-point correlation functions are used throughout cosmology as a
measure for the statistics of random fields. When used in Bayesian parameter
estimation, their likelihood function is usually replaced by a Gaussian
approximation. However, this has been shown to be insufficient.
Aims: For the case of Gaussian random fields, we search for an exact
probability distribution of correlation functions, which could improve the
accuracy of future data analyses.
Methods: We use a fully analytic approach, first expanding the random field
in its Fourier modes, and then calculating the characteristic function.
Finally, we derive the probability distribution function using integration by
residues. We use a numerical implementation of the full analytic formula to
discuss the behaviour of this function.
Results: We derive the univariate and bivariate probability distribution
function of the correlation functions of a Gaussian random field, and outline
how higher joint distributions could be calculated. We give the results in the
form of mode expansions, but in one special case we also find a closed-form
expression. We calculate the moments of the distribution and, in the univariate
case, we discuss the Edgeworth expansion approximation. We also comment on the
difficulties in a fast and exact numerical implementation of our results, and
on possible future applications.Comment: 13 pages, 5 figures, updated to match version published in A&A
(slightly expanded Sects. 5.3 and 6
Standard and non-standard primordial neutrinos
The standard cosmological model predicts the existence of a cosmic neutrino
background with a present density of about 110 cm^{-3} per flavour, which
affects big-bang nucleosynthesis, cosmic microwave background anisotropies, and
the evolution of large scale structures. We report on a precision calculation
of the cosmic neutrino background properties including the modification
introduced by neutrino oscillations. The role of a possible
neutrino-antineutrino asymmetry and the impact of non-standard
neutrino-electron interactions on the relic neutrinos are also briefly
discussed.Comment: 4 pages, no figures. Contribution to the proceedings of SNOW 2006,
Stockholm, May 2-6, 2006. Typos corrected, updated reference
Power Spectra in Global Defect Theories of Cosmic Structure Formation
An efficient technique for computing perturbation power spectra in field
ordering theories of cosmic structure formation is introduced, enabling
computations to be carried out with unprecedented precision. Large scale
simulations are used to measure unequal time correlators of the source stress
energy, taking advantage of scaling during matter and radiation domination, and
causality, to make optimal use of the available dynamic range. The correlators
are then re-expressed in terms of a sum of eigenvector products, a
representation which we argue is optimal, enabling the computation of the final
power spectra to be performed at high accuracy. Microwave anisotropy and matter
perturbation power spectra for global strings, monopoles, textures and
non-topological textures are presented and compared with recent observations.Comment: 4 pages, compressed and uuencoded RevTex file and postscript figure
Classification of singular points in polarization field of CMB and eigenvectors of Stokes matrix
Analysis of the singularities of the polarization field of CMB, where
polarization is equal to zero, is presented. It is found that the
classification of the singular points differs from the usual three types known
in the ordinary differential equations. The new statistical properties of
polarization field are discussed, and new methods to detect the presence of
primordial tensor perturbations are indicated.Comment: 7 pages, 1 figure
Direct Signature of Evolving Gravitational Potential from Cosmic Microwave Background
We show that time dependent gravitational potential can be directly detected
from the cosmic microwave background (CMB) anisotropies. The signature can be
measured by cross-correlating the CMB with the projected density field
reconstructed from the weak lensing distortions of the CMB itself. The
cross-correlation gives a signal whenever there is a time dependent
gravitational potential. This method traces dark matter directly and has a well
defined redshift distribution of the window projecting over the density
perturbations, thereby avoiding the problems plaguing other proposed
cross-correlations. We show that both MAP and Planck will be able to probe this
effect for observationally relevant curvature and cosmological constant models,
which will provide additional constraints on the cosmological parameters.Comment: 4 pages, 2 figures. Submitted to PR
Flow Annealed Kalman Inversion for Gradient-Free Inference in Bayesian Inverse Problems
For many scientific inverse problems we are required to evaluate an expensive
forward model. Moreover, the model is often given in such a form that it is
unrealistic to access its gradients. In such a scenario, standard Markov Chain
Monte Carlo algorithms quickly become impractical, requiring a large number of
serial model evaluations to converge on the target distribution. In this paper
we introduce Flow Annealed Kalman Inversion (FAKI). This is a generalization of
Ensemble Kalman Inversion (EKI), where we embed the Kalman filter updates in a
temperature annealing scheme, and use normalizing flows (NF) to map the
intermediate measures corresponding to each temperature level to the standard
Gaussian. In doing so, we relax the Gaussian ansatz for the intermediate
measures used in standard EKI, allowing us to achieve higher fidelity
approximations to non-Gaussian targets. We demonstrate the performance of FAKI
on two numerical benchmarks, showing dramatic improvements over standard EKI in
terms of accuracy whilst accelerating its already rapid convergence properties
(typically in steps).Comment: 9 pages, 2 figues. Presented at MaxEnt 2023. Modified version to
appear in MaxEnt 2023 proceeding
Detecting the Earliest Galaxies Through Two New Sources of 21cm Fluctuations
The first galaxies that formed at a redshift ~20-30 emitted continuum photons
with energies between the Lyman-alpha and Lyman limit wavelengths of hydrogen,
to which the neutral universe was transparent except at the Lyman-series
resonances. As these photons redshifted or scattered into the Lyman-alpha
resonance they coupled the spin temperature of the 21cm transition of hydrogen
to the gas temperature, allowing it to deviate from the microwave background
temperature. We show that the fluctuations in the radiation emitted by the
first galaxies produced strong fluctuations in the 21cm flux before the
Lyman-alpha coupling became saturated. The fluctuations were caused by biased
inhomogeneities in the density of galaxies, along with Poisson fluctuations in
the number of galaxies. Observing the power-spectra of these two sources would
probe the number density of the earliest galaxies and the typical mass of their
host dark matter halos. The enhanced amplitude of the 21cm fluctuations from
the era of Lyman-alpha coupling improves considerably the practical prospects
for their detection.Comment: 11 pages, 7 figures, ApJ, published. Normalization fixed in top
panels of Figures 4-
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