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Register a new userCosmic Shear Covariance Matrix in $w$CDM: Cosmology Matters
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Joachim Harnois-Deraps
Publication date
2019
fields
Physics
and research's language is
English
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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 sample the $[Omega_{rm m}, sigma_8, h, w_0]$ parameter space at 25 points organised in a Latin hyper-cube, spanning a range that contains most of the $2sigma$ posterior distribution from ongoing lensing surveys. At each of these nodes we evolve a pair of $N$-body simulations in which the sampling variance is highly suppressed, and ray-trace the volumes 800 times to further increase the effective sky coverage. We extract 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 $w$CDM models, we probe 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.
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Cosmic shear is the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Such images are coherently deformed by the tidal field of matter inhomogeneities along the line of sight. By measuring galaxy shape correlations, we can study the properties and evolution of structure on large scales as well as the geometry of the Universe. Thus, cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. We review here the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then we give an overview of weak-lensing measurements, and present the main observational cosmic-shear results since it was discovered 15 years ago, as well as the implications for cosmology. We then conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.
We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find $sigma_8 (Omega_{rm m}/0.3)^{0.5} = 0.81 pm 0.06$ (68% confidence), after marginalising over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About $20$% of our error bar comes from marginalising over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both datasets. Our uncertainties are $sim$30% larger than those from CFHTLenS when we carry out a comparable analysis of the two datasets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of $sigma_8 (Omega_{rm m}/0.3)^{0.5}$ is present regardless of the value of $w$.
The homogeneous, isotropic, and flat $Lambda$CDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special and general relativity. We present simple derivations of the most useful equations connecting astronomical observables (redshift, flux density, angular diameter, brightness, local space density,...) with the corresponding intrinsic properties of distant sources (lookback time, distance, spectral luminosity, linear size, specific intensity, source counts,...). We also present an analytic equation for lookback time that is accurate within 0.1% for all redshifts $z$. The exact equation for comoving distance is an elliptic integral that must be evaluated numerically, but we found a simple approximation with errors $< 0.2$% for all redshifts up to $z approx 50$.
With the advent of large-scale weak lensing surveys there is a need to understand how realistic, scale-dependent systematics bias cosmic shear and dark energy measurements, and how they can be removed. Here we describe how spatial variations in the amplitude and orientation of realistic image distortions convolve with the measured shear field, mixing the even-parity convergence and odd-parity modes, and bias the shear power spectrum. Many of these biases can be removed by calibration to external data, the survey itself, or by modelling in simulations. The uncertainty in the calibration must be marginalised over and we calculate how this propagates into parameter estimation, degrading the dark energy Figure-of-Merit. We find that noise-like biases affect dark energy measurements the most, while spikes in the bias power have the least impact, reflecting their correlation with the effect of cosmological parameters. We argue that in order to remove systematic biases in cosmic shear surveys and maintain statistical power effort should be put into improving the accuracy of the bias calibration rather than minimising the size of the bias. In general, this appears to be a weaker condition for bias removal. We also investigate how to minimise the size of the calibration set for a fixed reduction in the Figure-of-Merit. These results can be used to model the effect of biases and calibration on a cosmic shear survey accurately, assess their impact on the measurement of modified gravity and dark energy models, and to optimise surveys and calibration requirements.
(Abridged) We investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These {it 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 5 per cent for the shear correlation function $xi_{+}(theta)$ and its error. We find that the most important quantities for FS modelling is the ratio between the measured angle $theta$ and the angular size of the simulation box at the source redshift, $theta_{box}(z_s)$, or the multipole equivalent $ell / ell_{box}(z_s)$. When this ratio reaches 0.1, independently of the source redshift, the shear correlation function $xi_+$ is suppressed by 5, 10, 20 and 25 percent for $L_{box}= 1000$, $500$, $250$ and $147mbox{Mpc}/h$ respectively. When it reaches 0.2, the suppression exceeds 25 percent even for the largest box. The same effect is observed in $xi_{-}(theta)$, but at much larger angles. This has important consequences for cosmological analyses using $N$-body simulations to calibrate the impact of non-linear gravitational clustering or to estimate errors and systematics effects, and should not be overlooked. We propose simple semi-analytic solutions to correct for these finite box effects with and without the presence of survey masks, and the method can be generalized to any weak lensing estimator. This offers a graceful solution to the important problem of estimating accurate covariance matrices for weak lensing studies: there is no need to run extra large simulation volumes, as long as the box effects are corrected.
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