450 research outputs found
Measuring dark energy properties with 3D cosmic shear
We present parameter estimation forecasts for present and future 3D cosmic
shear surveys. We demonstrate that, in conjunction with results from cosmic
microwave background (CMB) experiments, the properties of dark energy can be
estimated with very high precision with large-scale, fully 3D weak lensing
surveys. In particular, a 5-band, 10,000 square degree ground-based survey to a
median redshift of zm=0.7 could achieve 1- marginal statistical errors,
in combination with the constraints expected from the CMB Planck Surveyor, of
w0=0.108 and wa=0.099 where we parameterize w by
w(a)=w0+wa(1-a) where a is the scale factor. Such a survey is achievable with a
wide-field camera on a 4 metre class telescope. The error on the value of w at
an intermediate pivot redshift of z=0.368 is constrained to
w(z=0.368)=0.0175. We compare and combine the 3D weak lensing
constraints with the cosmological and dark energy parameters measured from
planned Baryon Acoustic Oscillation (BAO) and supernova Type Ia experiments,
and find that 3D weak lensing significantly improves the marginalized errors. A
combination of 3D weak lensing, CMB and BAO experiments could achieve
w0=0.037 and wa=0.099. Fully 3D weak shear analysis avoids the
loss of information inherent in tomographic binning, and we show that the
sensitivity to systematic errors is much less. In conjunction with the fact
that the physics of lensing is very soundly based, this analysis demonstrates
that deep, wide-angle 3D weak lensing surveys are extremely promising for
measuring dark energy properties.Comment: 18 pages, 16 figures. Accepted to MNRAS. Figures now in grayscale.
Further discussions on non-Gaussianity and photometric redshift errors. Some
references adde
Wide Angle Redshift Distortions Revisited
We explore linear redshift distortions in wide angle surveys from the point
of view of symmetries. We show that the redshift space two-point correlation
function can be expanded into tripolar spherical harmonics of zero total
angular momentum . The
coefficients of the expansion are analogous to the 's of
the angular power spectrum, and express the anisotropy of the redshift space
correlation function. Moreover, only a handful of are
non-zero: the resulting formulae reveal a hidden simplicity comparable to
distant observer limit. The depend on spherical Bessel
moments of the power spectrum and . In the plane parallel
limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered.
The general formalism is used to derive useful new expressions. We present a
particularly simple trigonometric polynomial expansion, which is arguably the
most compact expression of wide angle redshift distortions. These formulae are
suitable to inversion due to the orthogonality of the basis functions. An
alternative Legendre polynomial expansion was obtained as well. This can be
shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity
of the underlying theory will admit similar calculations for higher order
statistics as well.Comment: 6 pages, 1 figure, ApJL submitte
Fast sampling from Wiener posteriors for image data with dataflow engines
We use Dataflow Engines (DFE) to construct an efficient Wiener filter of noisy and incomplete image data, and to quickly draw probabilistic samples of the compatible true underlying images from the Wiener posterior. Dataflow computing is a powerful approach using reconfigurable hardware, which can be deeply pipelined and is intrinsically parallel. The unique Wiener-filtered image is the minimum-variance linear estimate of the true image (if the signal and noise covariances are known) and the most probable true image (if the signal and noise are Gaussian distributed). However, many images are compatible with the data with different probabilities, given by the analytic posterior probability distribution referred to as the Wiener posterior. The DFE code also draws large numbers of samples of true images from this posterior, which allows for further statistical analysis. Naive computation of the Wiener-filtered image is impractical for large datasets, as it scales as [Formula presented], where [Formula presented] is the number of pixels. We use a messenger field algorithm, which is well suited to a DFE implementation, to draw samples from the Wiener posterior, that is, with the correct probability we draw samples of noiseless images that are compatible with the observed noisy image. The Wiener-filtered image can be obtained by a trivial modification of the algorithm. We demonstrate a lower bound on the speed-up, from drawing [Formula presented] samples of a [Formula presented] image, of 11.3 ± 0.8 with 8 DFEs in a 1U MPC-X box when compared with a 1U server presenting 32 CPU threads. We also discuss a potential application in astronomy, to provide better dark matter maps and improved determination of the parameters of the Universe
Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
Since cosmology is no longer "the data-starved science", the problem of how
to best analyze large data sets has recently received considerable attention,
and Karhunen-Loeve eigenvalue methods have been applied to both galaxy redshift
surveys and Cosmic Microwave Background (CMB) maps. We present a comprehensive
discussion of methods for estimating cosmological parameters from large data
sets, which includes the previously published techniques as special cases. We
show that both the problem of estimating several parameters jointly and the
problem of not knowing the parameters a priori can be readily solved by adding
an extra singular value decomposition step.
It has recently been argued that the information content in a sky map from a
next generation CMB satellite is sufficient to measure key cosmological
parameters (h, Omega, Lambda, etc) to an accuracy of a few percent or better -
in principle. In practice, the data set is so large that both a brute force
likelihood analysis and a direct expansion in signal-to-noise eigenmodes will
be computationally unfeasible. We argue that it is likely that a Karhunen-Loeve
approach can nonetheless measure the parameters with close to maximal accuracy,
if preceded by an appropriate form of quadratic "pre-compression".
We also discuss practical issues regarding parameter estimation from present
and future galaxy redshift surveys, and illustrate this with a generalized
eigenmode analysis of the IRAS 1.2 Jy survey optimized for measuring
beta=Omega^{0.6}/b using redshift space distortions.Comment: 15 pages, with 5 figures included. Substantially expanded with worked
COBE examples for e.g. the multiparameter case. Available from
http://www.sns.ias.edu/~max/karhunen.html (faster from the US), from
http://www.mpa-garching.mpg.de/~max/karhunen.html (faster from Europe) or
from [email protected]
Design and analysis of redshift surveys
In this paper we consider methods of analysis and optimal design of redshift
surveys. In the first part, we develop a formalism for analysing galaxy
redshift surveys which are essentially two-dimensional, such as thin
declination slices. The formalism is a power spectrum method, using spherical
coordinates, allowing the distorting effects of galaxy peculiar velocities to
be calculated to linear order on the assumption of statistical isotropy but
without further approximation. In this paper, we calculate the measured
two-dimensional power for a constant declination strip, widely used in redshift
surveys. We present a likelihood method for estimating the three-dimensional
real-space power spectrum and the redshift distortion simultaneously, and show
that for thin surveys of reasonable depth, the large-scale 3D power cannot be
measured with high accuracy. The redshift distortion may be estimated
successfully, and with higher accuracy if the 3D power spectrum can be measured
independently, for example from a large-scale sky-projected catalogue. In the
second part, we show how a 3D survey design can be optimized to measure the
power spectrum, considering whether areal coverage is more important than
depth, and whether the survey should be sampled sparsely or not. We show quite
generally that width is better than depth, and show how the optimal
sparse-sampling fraction, f, depends on the power, P, to be measured. For a
Schechter luminosity function, a simple optimization fP \simeq 500 h^{-3} Mpc^3
is found.Comment: 9 pages (Latex), 6 postscript figures included, MNRAS in pres
Cosmological constraints from COMBO-17 using 3D weak lensing
We present the first application of the 3D cosmic shear method developed in
Heavens et al. (2006) and the geometric shear-ratio analysis developed in
Taylor et al. (2006), to the COMBO-17 data set. 3D cosmic shear has been used
to analyse galaxies with redshift estimates from two random COMBO-17 fields
covering 0.52 square degrees in total, providing a conditional constraint in
the (sigma_8, Omega_m) plane as well as a conditional constraint on the
equation of state of dark energy, parameterised by a constant w= p/rho c^2. The
(sigma_8, Omega_m) plane analysis constrained the relation between sigma_8 and
Omega_m to be sigma_8(Omega_m/0.3)^{0.57 +- 0.19}=1.06 +0.17 -0.16, in
agreement with a 2D cosmic shear analysis of COMBO-17. The 3D cosmic shear
conditional constraint on w using the two random fields is w=-1.27 +0.64 -0.70.
The geometric shear-ratio analysis has been applied to the A901/2 field, which
contains three small galaxy clusters. Combining the analysis from the A901/2
field, using the geometric shear-ratio analysis, and the two random fields,
using 3D cosmic shear, w is conditionally constrained to w=-1.08 +0.63 -0.58.
The errors presented in this paper are shown to agree with Fisher matrix
predictions made in Heavens et al. (2006) and Taylor et al. (2006). When these
methods are applied to large datasets, as expected soon from surveys such as
Pan-STARRS and VST-KIDS, the dark energy equation of state could be constrained
to an unprecedented degree of accuracy.Comment: 10 pages, 4 figures. Accepted to MNRA
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