42 research outputs found
Sparsely Sampling the Sky: A Bayesian Experimental Design Approach
The next generation of galaxy surveys will observe millions of galaxies over
large volumes of the universe. These surveys are expensive both in time and
cost, raising questions regarding the optimal investment of this time and
money. In this work we investigate criteria for selecting amongst observing
strategies for constraining the galaxy power spectrum and a set of cosmological
parameters. Depending on the parameters of interest, it may be more efficient
to observe a larger, but sparsely sampled, area of sky instead of a smaller
contiguous area. In this work, by making use of the principles of Bayesian
Experimental Design, we will investigate the advantages and disadvantages of
the sparse sampling of the sky and discuss the circumstances in which a sparse
survey is indeed the most efficient strategy. For the Dark Energy Survey (DES),
we find that by sparsely observing the same area in a smaller amount of time,
we only increase the errors on the parameters by a maximum of 0.45%.
Conversely, investing the same amount of time as the original DES to observe a
sparser but larger area of sky we can in fact constrain the parameters with
errors reduced by 28%
True CMB Power Spectrum Estimation
The cosmic microwave background (CMB) power spectrum is a powerful
cosmological probe as it entails almost all the statistical information of the
CMB perturbations. Having access to only one sky, the CMB power spectrum
measured by our experiments is only a realization of the true underlying
angular power spectrum. In this paper we aim to recover the true underlying CMB
power spectrum from the one realization that we have without a need to know the
cosmological parameters. The sparsity of the CMB power spectrum is first
investigated in two dictionaries; Discrete Cosine Transform (DCT) and Wavelet
Transform (WT). The CMB power spectrum can be recovered with only a few
percentage of the coefficients in both of these dictionaries and hence is very
compressible in these dictionaries. We study the performance of these
dictionaries in smoothing a set of simulated power spectra. Based on this, we
develop a technique that estimates the true underlying CMB power spectrum from
data, i.e. without a need to know the cosmological parameters. This smooth
estimated spectrum can be used to simulate CMB maps with similar properties to
the true CMB simulations with the correct cosmological parameters. This allows
us to make Monte Carlo simulations in a given project, without having to know
the cosmological parameters. The developed IDL code, TOUSI, for Theoretical
pOwer spectrUm using Sparse estImation, will be released with the next version
of ISAP
Propagating Residual Biases in Cosmic Shear Power Spectra
In this paper we derive a full expression for the propagation of
multiplicative and additive shape measurement biases into the cosmic shear
power spectrum. In doing so we identify several new terms that are associated
with selection effects, as well as cross-correlation terms between the
multiplicative and additive biases and the shear field. The computation of the
resulting bias in the shear power spectrum scales as the fifth power of the
maximum multipole considered. Consequently the calculation is unfeasible for
large l-modes, and the only tractable way to assess the full impact of shape
measurement biases on cosmic shear power spectrum is through forward modelling
of the effects. To linear order in bias parameters the shear power spectrum is
only affected by the mean of the multiplicative bias field over a survey and
the cross correlation between the additive bias field and the shear field. If
the mean multiplicative bias is zero then second order convolutive terms are
expected to be orders of magnitude smaller.Comment: 10 pages, accepted to the Open Journal of Astrophysic
Joint Planck and WMAP CMB Map Reconstruction
We present a novel estimate of the cosmological microwave background (CMB)
map by combining the two latest full-sky microwave surveys: WMAP nine-year and
Planck PR1. The joint processing benefits from a recently introduced component
separation method coined "local-generalized morphological component analysis''
(LGMCA) based on the sparse distribution of the foregrounds in the wavelet
domain. The proposed estimation procedure takes advantage of the IRIS 100
micron as an extra observation on the galactic center for enhanced dust
removal. We show that this new CMB map presents several interesting aspects: i)
it is a full sky map without using any inpainting or interpolating method, ii)
foreground contamination is very low, iii) the Galactic center is very clean,
with especially low dust contamination as measured by the cross-correlation
between the estimated CMB map and the IRIS 100 micron map, and iv) it is free
of thermal SZ contamination.Comment: Astronomy and Astrophysics, accepte
Planck CMB Anomalies: Astrophysical and Cosmological Secondary Effects and the Curse of Masking
Large-scale anomalies have been reported in CMB data with both WMAP and
Planck data. These could be due to foreground residuals and or systematic
effects, though their confirmation with Planck data suggests they are not due
to a problem in the WMAP or Planck pipelines. If these anomalies are in fact
primordial, then understanding their origin is fundamental to either validate
the standard model of cosmology or to explore new physics. We investigate three
other possible issues: 1) the trade-off between minimising systematics due to
foreground contamination (with a conservative mask) and minimising systematics
due to masking, 2) astrophysical secondary effects (the kinetic Doppler
quadrupole and kinetic Sunyaev-Zel'dovich effect), and 3) secondary
cosmological signals (the integrated Sachs-Wolfe effect). We address the
masking issue by considering new procedures that use both WMAP and Planck to
produce higher quality full-sky maps using the sparsity methodology (LGMCA
maps). We show the impact of masking is dominant over that of residual
foregrounds, and the LGMCA full-sky maps can be used without further processing
to study anomalies. We consider four official Planck PR1 and two LGMCA CMB
maps. Analysis of the observed CMB maps shows that only the low quadrupole and
quadrupole-octopole alignment seem significant, but that the planar octopole,
Axis of Evil, mirror parity and cold spot are not significant in nearly all
maps considered. After subtraction of astrophysical and cosmological secondary
effects, only the low quadrupole may still be considered anomalous, meaning the
significance of only one anomaly is affected by secondary effect subtraction
out of six anomalies considered. In the spirit of reproducible research all
reconstructed maps and codes will be made available for download here
http://www.cosmostat.org/anomaliesCMB.html.Comment: Summary of results given in Table 2. Accepted for publication in
JCAP, 4th August 201
PRISM: Sparse Recovery of the Primordial Power Spectrum
The primordial power spectrum describes the initial perturbations in the
Universe which eventually grew into the large-scale structure we observe today,
and thereby provides an indirect probe of inflation or other
structure-formation mechanisms. Here, we introduce a new method to estimate
this spectrum from the empirical power spectrum of cosmic microwave background
(CMB) maps.
A sparsity-based linear inversion method, coined \textbf{PRISM}, is
presented. This technique leverages a sparsity prior on features in the
primordial power spectrum in a wavelet basis to regularise the inverse problem.
This non-parametric approach does not assume a strong prior on the shape of the
primordial power spectrum, yet is able to correctly reconstruct its global
shape as well as localised features. These advantages make this method robust
for detecting deviations from the currently favoured scale-invariant spectrum.
We investigate the strength of this method on a set of WMAP 9-year simulated
data for three types of primordial power spectra: a nearly scale-invariant
spectrum, a spectrum with a small running of the spectral index, and a spectrum
with a localised feature. This technique proves to easily detect deviations
from a pure scale-invariant power spectrum and is suitable for distinguishing
between simple models of the inflation. We process the WMAP 9-year data and
find no significant departure from a nearly scale-invariant power spectrum with
the spectral index .
A high resolution primordial power spectrum can be reconstructed with this
technique, where any strong local deviations or small global deviations from a
pure scale-invariant spectrum can easily be detected
Propagating Residual Biases in Cosmic Shear Power Spectra
In this paper we derive a full expression for the propagation of multiplicative and additive shape measurement biases into the cosmic shear power spectrum. In doing so we identify several new terms that are associated with selection effects, as well as cross-correlation terms between the multiplicative and additive biases and the shear field. The computation of the resulting bias in the shear power spectrum scales as the fifth power of the maximum multipole considered. Consequently the calculation is unfeasible for large l-modes, and the only tractable way to assess the full impact of shape measurement biases on cosmic shear power spectrum is through forward modelling of the effects. To linear order in bias parameters the shear power spectrum is only affected by the mean of the multiplicative bias field over a survey and the cross correlation between the additive bias field and the shear field. If the mean multiplicative bias is zero then second order convolutive terms are expected to be orders of magnitude smaller
Sparsely sampling the sky: Regular vs. random sampling
International audienceAims. The next generation of galaxy surveys, aiming to observe millions of galaxies, are expensive both in time and money. This raises questions regarding the optimal investment of this time and money for future surveys. In a previous work, we have shown that a sparse sampling strategy could be a powerful substitute for the – usually favoured – contiguous observation of the sky. In our previous paper, regular sparse sampling was investigated, where the sparse observed patches were regularly distributed on the sky. The regularity of the mask introduces a periodic pattern in the window function, which induces periodic correlations at specific scales. Methods. In this paper, we use a Bayesian experimental design to investigate a “random” sparse sampling approach, where the observed patches are randomly distributed over the total sparsely sampled area. Results. We find that in this setting, the induced correlation is evenly distributed amongst all scales as there is no preferred scale in the window function. Conclusions. This is desirable when we are interested in any specific scale in the galaxy power spectrum, such as the matter-radiation equality scale. As the figure of merit shows, however, there is no preference between regular and random sampling to constrain the overall galaxy power spectrum and the cosmological parameters