158 research outputs found
Simulations of weak gravitational lensing â II. Including finite support effects in cosmic shear covariance matrices
Numerical N-body simulations play a central role in the assessment of weak gravitational lensing statistics, residual systematics and error analysis. In this paper, we investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These finite support (FS) effects are modelled for several estimators, simulation box sizes and source redshifts, and validated against a new large suite of 500 N-body simulations. The comparison reveals that our theoretical model is accurate to better than 5âperâcent for the shear correlation function Ο+(Ξ) and its error. We find that the most important quantities for FS modelling are the ratio between the measured angle Ξ and the angular size of the simulation box at the source redshift, Ξbox(zs), or the multipole equivalent â/âbox(zs). When this ratio reaches 0.1, independently of the source redshift, the shear correlation function Ο+ is suppressed by 5, 10, 20 and 25âperâcent for Lbox = 1000, 500, 250 and 147âhâ1âMpc, respectively. The same effect is observed in Οâ(Ξ), but at much larger angles. This has important consequences for cosmological analyses using N-body simulations and should not be overlooked. We propose simple semi-analytic correction strategies that account for shape noise and survey masks, generalizable to any weak lensing estimator. From the same simulation suite, we revisit the existing non-Gaussian covariance matrix calibration of the shear correlation function, and propose a new one based on the 9-year Wilkinson Microwave Anisotropy Probe)+baryon acoustic oscillations+supernova cosmology. Our calibration matrix is accurate at 20âperâcent down to the arcminute scale, for source redshifts in the range 0 < z < 3, even for the far off-diagonal elements. We propose, for the first time, a parametrization for the full Οâ covariance matrix, also 20âperâcent accurate for most elements
Cosmic shear covariance matrix in wCDM: Cosmology matters
We present here the cosmo-SLICS, a new suite of simulations specially designed for the analysis of current and upcoming weak lensing data beyond the standard two-point cosmic shear. We sampled the [Ωm,âÏ8,âh,âw0] parameter space at 25 points organised in a Latin hyper-cube, spanning a range that contains most of the 2Ï posterior distribution from ongoing lensing surveys. At each of these nodes we evolved a pair of N-body simulations in which the sampling variance is highly suppressed, and ray-traced the volumes 800 times to further increase the effective sky coverage. We extracted a lensing covariance matrix from these pseudo-independent light-cones and show that it closely matches a brute-force construction based on an ensemble of 800 truly independent N-body runs. More precisely, a Fisher analysis reveals that both methods yield marginalized two-dimensional constraints that vary by less than 6% in area, a result that holds under different survey specifications and that matches to within 15% the area obtained from an analytical covariance calculation. Extending this comparison with our 25 wCDM models, we probed the cosmology dependence of the lensing covariance directly from numerical simulations, reproducing remarkably well the Fisher results from the analytical models at most cosmologies. We demonstrate that varying the cosmology at which the covariance matrix is evaluated in the first place might have an order of magnitude greater impact on the parameter constraints than varying the choice of covariance estimation technique. We present a test case in which we generate fast predictions for both the lensing signal and its associated variance with a flexible Gaussian process regression emulator, achieving an accuracy of a few percent on the former and 10% on the latter
The skewed weak lensing likelihood: why biases arise, despite data and theory being sound
We derive the essentials of the skewed weak lensing likelihood via a simple hierarchical forward model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of Lambda cold dark matter. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from cosmic microwave background analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30âperâcent of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses
Persistent homology in cosmic shear: constraining parameters with topological data analysis
In recent years, cosmic shear has emerged as a powerful tool to study the
statistical distribution of matter in our Universe. Apart from the standard
two-point correlation functions, several alternative methods like peak count
statistics offer competitive results. Here we show that persistent homology, a
tool from topological data analysis, can extract more cosmological information
than previous methods from the same dataset. For this, we use persistent Betti
numbers to efficiently summarise the full topological structure of weak lensing
aperture mass maps. This method can be seen as an extension of the peak count
statistics, in which we additionally capture information about the environment
surrounding the maxima. We first demonstrate the performance in a mock analysis
of the KiDS+VIKING-450 data: we extract the Betti functions from a suite of
CDM -body simulations and use these to train a Gaussian process emulator
that provides rapid model predictions; we next run a Markov-Chain Monte Carlo
analysis on independent mock data to infer the cosmological parameters and
their uncertainty. When comparing our results, we recover the input cosmology
and achieve a constraining power on that is 5% tighter than that of peak
count statistics. Performing the same analysis on 100 deg of Euclid-like
simulations, we are able to improve the constraints on and
by 18% and 10%, respectively, while breaking some of the
degeneracy between and the dark energy equation of state. To our
knowledge, the methods presented here are the most powerful topological tools
to constrain cosmological parameters with lensing data
A revised density split statistic model for general filters
Studying the statistical properties of the large-scale structure in the
Universe with weak gravitational lensing is a prime goal of several current and
forthcoming galaxy surveys. The power that weak lensing has to constrain
cosmological parameters can be enhanced by considering statistics beyond
second-order shear correlation functions or power spectra. One such
higher-order probe that has proven successful in observational data is the
density split statistics (DSS), in which one analyses the mean shear profiles
around points that are classified according to their foreground galaxy density.
In this paper, we generalise the most accurate DSS model to allow for a broad
class of angular filter functions used for the classification of the different
local density regions. This approach is motivated by earlier findings showing
that an optimised filter can provide tighter constraints on model parameters
compared to the standard top-hat case. We build on large deviation theory
approaches and approximations thereof to model the matter density PDF, and on
perturbative calculations of higher-order moments of the density field. The
novel addition relies on the generalisation of these previously employed
calculations to allow for general filter functions and is validated on several
sets of numerical simulations. The revised model fits well the simulation
measurements, with a residual systematic offset that is small compared to the
statistical accuracy of current weak lensing surveys. The accuracy of the model
is slightly lower for a compensated filter than for a non-negative filter
function, and that it increases with the filter size. Using a Fisher matrix
approach, we find constraints comparable to the commonly used two-point cosmic
shear measures. Hence, our DSS model can be used in competitive analyses of
current cosmic shear data, while it may need refinements for forthcoming
lensing surveys.Comment: 21 pages, 13 figure
On cosmological bias due to the magnification of shear and position samples in modern weak lensing analyses
The magnification of galaxies in modern galaxy surveys induces additional
correlations in the cosmic shear, galaxy-galaxy lensing and clustering
observables used in modern lensing "3x2pt" analyses, due to sample selection.
In this paper, we emulate the magnification contribution to all three
observables utilising the SLICS simulations suite, and test the sensitivity of
the cosmological model, galaxy bias and redshift distribution calibration to
un-modelled magnification in a Stage-IV-like survey using Monte-Carlo sampling.
We find that magnification cannot be ignored in any single or combined
observable, with magnification inducing biases in the
plane, including for cosmic shear and 3x2pt analyses. Significant cosmological
biases exist in the 3x2pt and cosmic shear from magnification of the shear
sample alone. We show that magnification induces significant biases in the mean
of the redshift distribution where a position sample is analysed, which may
potentially be used to identify contamination by magnification.Comment: 17 pages, 7 figures, 3 tables. Submitted to MNRAS. Comments welcom
Starlet higher order statistics for galaxy clustering and weak lensing
We present a first application to photometric galaxy clustering and weak
lensing of wavelet based multi-scale higher order summary statistics: starlet
peak counts and starlet -norm. Peak counts are the local maxima in the
map and the -norm is computed via the sum of the absolute values of the
starlet (wavelet) decomposition coefficients of a map, providing a fast
multi-scale calculation of the pixel distribution, encoding the information of
all pixels in the map. We employ the cosmo-SLICS simulations sources and lenses
catalogues and we compute wavelet based higher order statistics in the context
of combined probes and their potential when applied to the weak lensing
convergence maps and galaxy maps. We get forecasts on the matter density
parameter , the reduced Hubble constant , the matter
fluctuation amplitude , and the dark energy equation of state
parameter . We find that, in our setting for this first application,
considering the two probes as independent, starlet peaks and the -norm
represent interesting summary statistics that can improve the constraints with
respect to the power spectrum also in the case of photometric galaxy clustering
and when the two probes are combined.Comment: A&A Letters to the Editor, Forthcoming article, accepte
On the road to percent accuracy III: non-linear reaction of the matter power spectrum to massive neutrinos
We analytically model the non-linear effects induced by massive neutrinos on the total matter power spectrum using the halo model reaction framework of Cataneo et al. In this approach, the halo model is used to determine the relative change to the matter power spectrum caused by new physics beyond the concordance cosmology. Using standard fitting functions for the halo abundance and the halo massâconcentration relation, the total matter power spectrum in the presence of massive neutrinos is predicted to perâcent-level accuracy, out to k=10hMpcâ1â . We find that refining the prescriptions for the halo properties using N-body simulations improves the recovered accuracy to better than 1âperâcent. This paper serves as another demonstration for how the halo model reaction framework, in combination with a single suite of standard Î cold dark matter (ÎCDM) simulations, can recover perâcent-level accurate predictions for beyond ÎCDM matter power spectra, well into the non-linear regime
Non-Gaussianity in the Weak Lensing Correlation Function Likelihood -- Implications for Cosmological Parameter Biases
We study the significance of non-Gaussianity in the likelihood of weak
lensing shear two-point correlation functions, detecting significantly non-zero
skewness and kurtosis in one-dimensional marginal distributions of shear
two-point correlation functions in simulated weak lensing data. We examine the
implications in the context of future surveys, in particular LSST, with
derivations of how the non-Gaussianity scales with survey area. We show that
there is no significant bias in one-dimensional posteriors of
and due to the non-Gaussian likelihood distributions of shear
correlations functions using the mock data ( deg). We also present a
systematic approach to constructing approximate multivariate likelihoods with
one-dimensional parametric functions by assuming independence or more flexible
non-parametric multivariate methods after decorrelating the data points using
principal component analysis (PCA). While the use of PCA does not modify the
non-Gaussianity of the multivariate likelihood, we find empirically that the
one-dimensional marginal sampling distributions of the PCA components exhibit
less skewness and kurtosis than the original shear correlation
functions.Modeling the likelihood with marginal parametric functions based on
the assumption of independence between PCA components thus gives a lower limit
for the biases. We further demonstrate that the difference in cosmological
parameter constraints between the multivariate Gaussian likelihood model and
more complex non-Gaussian likelihood models would be even smaller for an
LSST-like survey. In addition, the PCA approach automatically serves as a data
compression method, enabling the retention of the majority of the cosmological
information while reducing the dimensionality of the data vector by a factor of
5.Comment: 16 pages, 10 figures, published MNRA
Dark matter distribution induced by a cosmic string wake in the nonlinear regime
We study the distribution of dark matter in the nonlinear regime in a model in which the primordial fluctuations include, in addition to the dominant primordial Gaussian fluctuations generated by the standard ÎCDMcosmological model, the effects of a cosmic string wake set up at the time of equal matter and radiation, making use of cosmological N-body simulations. At early times, the string wake leads to a planar overdensity of dark matter.We study how this non-Gaussian pattern of a cosmic string wake evolves in the presence of the Gaussian perturbations, making use of wavelet and ridgeletlike statistics specifically designed to extract string wake signals. At late times, the Gaussian fluctuations disrupt the string wake.We find that for a string tension ofGÎŒ ÂŒ 10â7, a value just belowthe current observational limit, the effects of a string wake can be identified in the dark matter distribution, using the current level of the statistical analysis, down to a redshift of z ÂŒ 10
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