50 research outputs found
The Angular Power Spectrum of the First-Year WMAP Data Reanalysed
We measure the angular power spectrum of the WMAP first-year temperature
anisotropy maps. We use SpICE (Spatially Inhomogeneous Correlation Estimator)
to estimate Cl's for multipoles l=2-900 from all possible cross-correlation
channels. Except for the map-making stage, our measurements provide an
independent analysis of that by Hinshaw etal (2003). Despite the different
methods used, there is virtually no difference between the two measurements for
l < 700 ; the highest l's are still compatible within 1-sigma errors. We use a
novel intra-bin variance method to constrain Cl errors in a model independent
way. When applied to WMAP data, the intra-bin variance estimator yields
diagonal errors 10% larger than those reported by the WMAP team for 100 < l <
450. This translates into a 2.4 sigma detection of systematics since no
difference is expected between the SpICE and the WMAP team estimator window
functions in this multipole range. With our measurement of the Cl's and errors,
we get chi^2/d.o.f. = 1.042 for a best-fit LCDM model, which has a 14%
probability, whereas the WMAP team obtained chi^2/d.o.f. = 1.066, which has a
5% probability. We assess the impact of our results on cosmological parameters
using Markov Chain Monte Carlo simulations. From WMAP data alone, assuming
spatially flat power law LCDM models, we obtain the reionization optical depth
tau = 0.145 +/- 0.067, spectral index n_s = 0.99 +/- 0.04, Hubble constant h =
0.67 +/- 0.05, baryon density Omega_b h^2 = 0.0218 +/- 0.0014, cold dark matter
density Omega_{cdm} h^2 = 0.122 +/- 0.018, and sigma_8 = 0.92 +/- 0.12,
consistent with a reionization redshift z_{re} = 16 +/- 5 (68% CL).Comment: Matches version accepted by ApJ Letters. Main changes: emphasizes
chi2 value for best-fit model given our estimate of Cls and errors vs. WMAP
team's. Potential detection of systematics in WMAP data quantified. Power
spectrum and other data files available at
http://www.ifa.hawaii.edu/cosmowave/wmap.htm
Holographic Quantum Statistics from Dual Thermodynamics
We propose dual thermodynamics corresponding to black hole mechanics with the
identifications E' -> A/4, S' -> M, and T' -> 1/T in Planck units. Here A, M
and T are the horizon area, mass and Hawking temperature of a black hole and
E', S' and T' are the energy, entropy and temperature of a corresponding dual
quantum system. We show that, for a Schwarzschild black hole, the dual
variables formally satisfy all three laws of thermodynamics, including the
Planck-Nernst form of the third law requiring that the entropy tend to zero at
low temperature. This is in contrast with traditional black hole
thermodynamics, where the entropy is singular. Once the third law is satisfied,
it is straightforward to construct simple (dual) quantum systems representing
black hole mechanics. As an example, we construct toy models from one
dimensional (Fermi or Bose) quantum gases with N ~ M in a Planck scale box. In
addition to recovering black hole mechanics, we obtain quantum corrections to
the entropy, including the logarithmic correction obtained by previous papers.
The energy-entropy duality transforms a strongly interacting gravitational
system (black hole) into a weakly interacting quantum system (quantum gas) and
thus provides a natural framework for the quantum statistics underlying the
holographic conjecture.Comment: 10 page
Constraining Primordial Non-Gaussianities from the WMAP2 2-1 Cumulant Correlator Power Spectrum
We measure the 2-1 cumulant correlator power spectrum , a
degenerate bispectrum, from the second data release of the Wilkinson Microwave
Anisotropy Probe (WMAP). Our high resolution measurements with SpICE span a
large configuration space () corresponding to the possible
cross-correlations of the maps recorded by the different differencing
assemblies. We present a novel method to recover the eigenmodes of the
correspondingly large Monte Carlo covariance matrix. We examine its eigenvalue
spectrum and use random matrix theory to show that the off diagonal terms are
dominated by noise. We minimize the to obtain constraints for the
non-linear coupling parameter .Comment: 4 pages,2 figures; typos corrected, references change
Optimal non-linear transformations for large scale structure statistics
Recently, several studies proposed non-linear transformations, such as a
logarithmic or Gaussianization transformation, as efficient tools to recapture
information about the (Gaussian) initial conditions. During non-linear
evolution, part of the cosmologically relevant information leaks out from the
second moment of the distribution. This information is accessible only through
complex higher order moments or, in the worst case, becomes inaccessible to the
hierarchy. The focus of this work is to investigate these transformations in
the framework of Fisher information using cosmological perturbation theory of
the matter field with Gaussian initial conditions. We show that at each order
in perturbation theory, there is a polynomial of corresponding order exhausting
the information on a given parameter. This polynomial can be interpreted as the
Taylor expansion of the maximally efficient "sufficient" observable in the
non-linear regime. We determine explicitly this maximally efficient observable
for local transformations. Remarkably, this optimal transform is essentially
the simple power transform with an exponent related to the slope of the power
spectrum; when this is -1, it is indistinguishable from the logarithmic
transform. This transform Gaussianizes the distribution, and recovers the
linear density contrast. Thus a direct connection is revealed between undoing
of the non-linear dynamics and the efficient capture of Fisher information. Our
analytical results were compared with measurements from the Millennium
Simulation density field. We found that our transforms remain very close to
optimal even in the deeply non-linear regime with \sigma^2 \sim 10.Comment: 11 pages, matches version accepted for publication in MNRA
Determining Bias with Cumulant Correlators
The first non-trivial cumulant correlator of the galaxy density field
is examined from the point of view of biasing. It is shown that to
leading order it depends on two biasing parameters , and , and on
, the underlying cumulant correlator of the mass. As the skewness
has analogous properties, the slope of the correlation function ,
, and uniquely determine the bias parameter on a particular scale
to be , when working in the context of gravitational
instability with Gaussian initial conditions. Thus on large scales, easily
accessible with the future Sloan Digital Sky Survey and the 2 Degree Field
Survey, it will be possible to extract , and from simple counts in
cells measurements. Moreover, the higher order cumulants, , successively
determine the higher order biasing parameters. From these it is possible to
predict higher order cumulant correlators as well. Comparing the predictions
with the measurements will provide internal consistency checks on the validity
of the assumptions in the theory, most notably perturbation theory of the
growth of fluctuations by gravity and Gaussian initial conditions. Since the
method is insensitive to , it can be successfully combined with results
from velocity fields, which determine , to measure the total
density parameter in the universe.Comment: 4 pages, submitted to MNRAS pink page
On Recovering the Nonlinear Bias Function from Counts in Cells Measurements
We present a simple and accurate method to constrain galaxy bias based on the
distribution of counts in cells. The most unique feature of our technique is
that it is applicable to non-linear scales, where both dark matter statistics
and the nature of galaxy bias are fairly complex. First, we estimate the
underlying continuous distribution function from precise counts-in-cells
measurements assuming local Poisson sampling. Then a robust, non-parametric
inversion of the bias function is recovered from the comparison of the
cumulative distributions in simulated dark matter and galaxy catalogs.
Obtaining continuous statistics from the discrete counts is the most delicate
novel part of our recipe. It corresponds to a deconvolution of a (Poisson)
kernel. For this we present two alternatives: a model independent algorithm
based on Richardson-Lucy iteration, and a solution using a parametric skewed
lognormal model. We find that the latter is an excellent approximation for the
dark matter distribution, but the model independent iterative procedure is more
suitable for galaxies. Tests based on high resolution dark matter simulations
and corresponding mock galaxy catalogs show that we can reconstruct the
non-linear bias function down to highly non-linear scales with high precision
in the range of . As far as the stochasticity of the bias,
we have found a remarkably simple and accurate formula based on Poisson noise,
which provides an excellent approximation for the scatter around the mean
non-linear bias function. In addition we have found that redshift distortions
have a negligible effect on our bias reconstruction, therefore our recipe can
be safely applied to redshift surveys.Comment: 32 pages, 18 figures; submitted to Ap
Supervoids in the WISE-2MASS catalogue imprinting Cold Spots in the Cosmic Microwave Background
The Cold Spot (CS) is a clear feature in the Cosmic Microwave Background
(CMB); it could be of primordial origin, or caused by a intervening structure
along the line of sight. We identified a large projected underdensity in the
recently constructed WISE-2MASS all-sky infrared galaxy catalogue aligned with
the Cold Spot direction at . It has an
angular size of tens of degrees, and shows a galaxy underdensity in
the center. Moreover, we find another large underdensity in the projected
WISE-2MASS galaxy map at (hereafter Draco
Supervoid), also aligned with a CMB decrement, although less significant than
that of the CS direction. Motivated by these findings, we develop spherically
symmetric Lemaitre-Tolman-Bondi (LTB) compensated void models to explain the
observed CMB decrements with these two underdensities, or "supervoids". Within
our perturbative treatment of the LTB voids, we find that the Integrated
Sachs-Wolfe and Riess-Sciama effects due to the Draco Supervoid can account for
the CMB decrement observed in the same direction. On the contrary, the
extremely deep CMB decrement in the CS direction is more difficult to explain
by the presence of the CS supervoid only. Nevertheless, the probability of a
random alignment between the CS and the corresponding supervoid is disfavored,
and thus its contribution as a secondary anisotropy cannot be neglected. We
comment on how the approximations used in this paper, in particular the
assumption of spherical symmetry, could change quantitatively our conclusions
and might provide a better explanation for the CMB CS.Comment: 12 pages, 11 figures, major revision, new results, resubmitted to
MNRA