Simulations of weak gravitational lensing – 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 5 per cent for the shear correlation function ξ+(θ) and its error. We find that the most important quantities for FS modelling are the ratio between the measured angle θ and the angular size of the simulation box at the source redshift, θbox(zs), or the multipole equivalent ℓ/ℓbox(zs). When this ratio reaches 0.1, independently of the source redshift, the shear correlation function ξ+ is suppressed by 5, 10, 20 and 25 per cent for Lbox = 1000, 500, 250 and 147 h−1 Mpc, respectively. The same effect is observed in ξ−(θ), 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 20 per cent 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 ξ− covariance matrix, also 20 per cent 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, σ8, h, w0] parameter space at 25 points organised in a Latin hyper-cube, spanning a range that contains most of the 2σ 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 30 per cent 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

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 $>1\sigma$ biases in the $w_0-\sigma_8$ 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

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 mass–concentration relation, the total matter power spectrum in the presence of massive neutrinos is predicted to per cent-level accuracy, out to k=10hMpc−1⁠. We find that refining the prescriptions for the halo properties using N-body simulations improves the recovered accuracy to better than 1 per cent. This paper serves as another demonstration for how the halo model reaction framework, in combination with a single suite of standard Λ cold dark matter (ΛCDM) simulations, can recover per cent-level accurate predictions for beyond ΛCDM matter power spectra, well into the non-linear regime

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 ΛCDMcosmological 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 ofGμ ¼ 10−7, 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 ¼ 10

Painting with baryons: augmenting N-body simulations with gas using deep generative models

Running hydrodynamical simulations to produce mock data of large-scale structure and baryonic probes, such as the thermal Sunyaev-Zeldovich (tSZ) effect, at cosmological scales is computationally challenging. We propose to leverage the expressive power of deep generative models to find an effective description of the large-scale gas distribution and temperature. We train two deep generative models, a variational auto-encoder and a generative adversarial network, on pairs of matter density and pressure slices from the BAHAMAS hydrodynamical simulation. The trained models are able to successfully map matter density to the corresponding gas pressure. We then apply the trained models on 100 lines-of-sight from SLICS, a suite of N-body simulations optimised for weak lensing covariance estimation, to generate maps of the tSZ effect. The generated tSZ maps are found to be statistically consistent with those from BAHAMAS. We conclude by considering a specific observable, the angular cross-power spectrum between the weak lensing convergence and the tSZ effect and its variance, where we find excellent agreement between the predictions from BAHAMAS and SLICS, thus enabling the use of SLICS for tSZ covariance estimation

Enhancing the cosmic shear power spectrum

Applying a transformation to a non-Gaussian field can enhance the information content of the resulting power spectrum, by reducing the correlations between Fourier modes. In the context of weak gravitational lensing, it has been shown that this gain in information content is significantly compromised by the presence of shape noise. We apply clipping to mock convergence fields, a technique which is known to be robust in the presence of noise and has been successfully applied to galaxy number density fields. When analysed in isolation the resulting convergence power spectrum returns degraded constraints on cosmological parameters. However, substantial gains can be achieved by performing a combined analysis of the power spectra derived from both the original and transformed fields. Even in the presence of realistic levels of shape noise, we demonstrate that this approach is capable of reducing the area of likelihood contours within the Ωm − σ8 plane by more than a factor of 3

Precision reconstruction of the cold dark matter-neutrino relative velocity fromN-body simulations

Discovering the mass of neutrinos is a principle goal in high energy physics and cosmology. In addition to cosmological measurements based on two-point statistics, the neutrino mass can also be estimated by observations of neutrino wakes resulting from the relative motion between cold dark matter (CDM) and neutrinos. Such a detection relies on an accurate reconstruction of the CDM-neutrino relative velocity which is affected by nonlinear structure growth and galaxy bias. We investigate our ability to reconstruct this relative velocity using large N-body simulations where we evolve neutrinos as distinct particles alongside the CDM. We find that the CDM velocity power spectrum is overpredicted by linear theory whereas the neutrino velocity power spectrum is underpredicted. The magnitude of the relative velocity observed in the simulations is found to be lower than what is predicted in linear theory. Since neither the CDM nor the neutrino velocity fields are directly observable from galaxy or 21 cm surveys, we test the accuracy of a reconstruction algorithm based on halo density fields and linear theory. Assuming prior knowledge of the halo bias, we find that the reconstructed relative velocities are highly correlated with the simulated ones with correlation coefficients of 0.94, 0.93, 0.92 and 0.88 for neutrinos of mass 0.05, 0.1, 0.2 and 0.4 eV. We confirm that the relative velocity field reconstructed from large scale structure observations such as galaxy or 21 cm surveys can be accurate in direction and, with appropriate scaling, magnitude

Testing modified gravity with cosmic shear

We use the cosmic shear data from the Canada–France–Hawaii Telescope Lensing Survey to place constraints on f(R) and Generalized Dilaton models of modified gravity. This is highly complementary to other probes since the constraints mainly come from the non-linear scales: maximal deviations with respects to the General Relativity (GR) + Λ cold dark matter (ΛCDM) scenario occurs at k ∼ 1 h Mpc−1. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parametrization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing ξ± quantity. Confronted against the cosmic shear data, we reject the f(R) {|fR0|=10−4,n=1} model with more than 99.9 per cent confidence interval (CI) when assuming a ΛCDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2 eV, the model is disfavoured with at least 94 per cent CI in all different combinations studied. Constraints on the {|fR0|=10−4,n=2} model are weaker, but nevertheless disfavoured with at least 89 per cent CI. We identify several specific combinations of neutrino mass, baryon feedback and f(R) or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data