279,336 research outputs found
Efficient Cosmological Parameter Estimation from Microwave Background Anisotropies
We revisit the issue of cosmological parameter estimation in light of current
and upcoming high-precision measurements of the cosmic microwave background
power spectrum. Physical quantities which determine the power spectrum are
reviewed, and their connection to familiar cosmological parameters is
explicated. We present a set of physical parameters, analytic functions of the
usual cosmological parameters, upon which the microwave background power
spectrum depends linearly (or with some other simple dependence) over a wide
range of parameter values. With such a set of parameters, microwave background
power spectra can be estimated with high accuracy and negligible computational
effort, vastly increasing the efficiency of cosmological parameter error
determination. The techniques presented here allow calculation of microwave
background power spectra times faster than comparably accurate direct
codes (after precomputing a handful of power spectra). We discuss various
issues of parameter estimation, including parameter degeneracies, numerical
precision, mapping between physical and cosmological parameters, and systematic
errors, and illustrate these considerations with an idealized model of the MAP
experiment.Comment: 22 pages, 12 figure
Estimation of Primordial Spectrum with post-WMAP 3 year data
In this paper we implement an improved (error sensitive) Richardson-Lucy
deconvolution algorithm on the measured angular power spectrum from the WMAP 3
year data to determine the primordial power spectrum assuming different points
in the cosmological parameter space for a flat LCDM cosmological model. We also
present the preliminary results of the cosmological parameter estimation by
assuming a free form of the primordial spectrum, for a reasonably large volume
of the parameter space. The recovered spectrum for a considerably large number
of the points in the cosmological parameter space has a likelihood far better
than a `best fit' power law spectrum up to \Delta \chi^2_{eff} \approx -30. We
use Discrete Wavelet Transform (DWT) for smoothing the raw recovered spectrum
from the binned data. The results obtained here reconfirm and sharpen the
conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp
cut off around the horizon scale and a bump after the horizon scale seem to be
a common feature for all of these reconstructed primordial spectra. We have
shown that although the WMAP 3 year data prefers a lower value of matter
density for a power law form of the primordial spectrum, for a free form of the
spectrum, we can get a very good likelihood to the data for higher values of
matter density. We have also shown that even a flat CDM model, allowing a free
form of the primordial spectrum, can give a very high likelihood fit to the
data. Theoretical interpretation of the results is open to the cosmology
community. However, this work provides strong evidence that the data retains
discriminatory power in the cosmological parameter space even when there is
full freedom in choosing the primordial spectrum.Comment: 13 pages, 4 figures, uses Revtex4, new analysis and results,
references added, matches version accepted to Phys. Rev.
Two-dimensional spectrum estimation using the radon transform
An alternative approach to two-dimensional power spectrum estimation incorporating the Radon transform in conjunction with each of the one-dimensional periodogram, Blackman-Tukey, and Autoregressive parameter estimation algorithms is examined. The Radon transform is used to express a two-dimensional data set in terms of its projections onto a set of one-dimensional radial lines, effectively reducing the two-dimensional estimation problem to a series of one-dimensional problems. The resulting two-dimensional power spectrum estimates are compared to the known power spectra for a variety of data types. The Radon transform approach combined with autoregressive parameter estimation can provide a high-resolution power spectrum estimate, effectively surpassing the resolution limitations of the Fourier methods without the cumbersome implementations of the more direct high resolution estimation methods in two dimensions
A Bayesian study of the primordial power spectrum from a novel closed universe model
We constrain the shape of the primordial power spectrum using recent
measurements of the cosmic microwave background (CMB) from the Wilkinson
Microwave Anisotropy Probe (WMAP) 7-year data and other high-resolution CMB
experiments. We also include observations of the matter power spectrum from the
luminous red galaxy (LRG) subset DR7 of the Sloan Digital Sky Survey (SDSS). We
consider two different models of the primordial power spectrum. The first is
the standard nearly scale-invariant spectrum in the form of a generalised
power-law parameterised in terms of the spectral amplitude , the
spectral index and (possibly) the running parameter .
The second spectrum is derived from the Lasenby and Doran (LD) model. The LD
model is based on the restriction of the total conformal time available in a
closed Universe and the predicted primordial power spectrum depends upon just
two parameters. An important feature of the LD spectrum is that it naturally
incorporates an exponential fall-off on large scales, which might provide a
possible explanation for the lower-than-expected power observed at low
multipoles in the CMB. In addition to parameter estimation, we compare both
models using Bayesian model selection. We find there is a significant
preference for the LD model over a simple power-law spectrum for a CMB-only
dataset, and over models with an equal number of parameters for all the
datasets considered.Comment: minor corrections to match accepted version to MNRA
Precise Estimation of Cosmological Parameters Using a More Accurate Likelihood Function
The estimation of cosmological parameters from a given data set requires a
construction of a likelihood function which, in general, has a complicated
functional form. We adopt a Gaussian copula and constructed a copula likelihood
function for the convergence power spectrum from a weak lensing survey. We show
that the parameter estimation based on the Gaussian likelihood erroneously
introduces a systematic shift in the confidence region, in particular for a
parameter of the dark energy equation of state w. Thus, the copula likelihood
should be used in future cosmological observations.Comment: 5 pages, 3 figures. Maches version published by the Physical Review
Letter
Fast Parameter Estimation from the CMB Power Spectrum
The statistical properties of a map of the primary fluctuations in the cosmic
microwave background (CMB) may be specified to high accuracy by a few thousand
power spectra measurements, provided the fluctuations are gaussian, yet the
number of parameters relevant for the CMB is probably no more than about 10-20.
There is consequently a large degree of redundancy in the power spectrum data.
In this paper, we show that the MOPED data compression technique can reduce the
CMB power spectrum measurements to about 10-20 numbers (one for each
parameter), from which the cosmological parameters can be estimated virtually
as accurately as from the complete power spectrum. This offers opportunities
for very fast parameter estimation from real and simulated CMB skies, with
accurate likelihood calculations at Planck resolution being speeded up by a
factor of around five hundred million.Comment: version to appear in MNRA
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