Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing

Abstract

Context. Weak-lensing surveys need accurate theoretical predictions for interpretation of their results and cosmological-parameter estimation. Aims. We study the accuracy of various approximations to cosmic shear and weak galaxy-galaxy lensing and investigate effects of Born corrections and lens-lens coupling. Methods. We use ray-tracing through the Millennium Simulation, a large N-body simulation of cosmic structure formation, to calculate various cosmic-shear and galaxy-galaxy-lensing statistics. We compare the results from ray-tracing to semi-analytic predictions. Results. (i) We confirm that the first-order approximation (i.e. neglecting lensing effects beyond first order in density fluctuations) provides an excellent fit to cosmic-shear power spectra as long as the actual matter power spectrum is used as input. Common fitting formulae, however, strongly underestimate the cosmic-shear power spectra (by >30% on scales > 10 000). Halo models provide a better fit to cosmic shear-power spectra, but there are still noticeable deviations (∼10%). (ii) Cosmic-shear B-modes, which are induced by Born corrections and lens-lens coupling, are at least three orders of magnitude smaller than cosmic-shear E-modes. Semianalytic extensions to the first-order approximation predict the right order of magnitude for the B-mode. Compared to the ray-tracing results, however, the semi-analytic predictions may differ by a factor two on small scales and also show a different scale dependence. (iii) The first-order approximation may under-or overestimate the galaxy-galaxy-lensing shear signal by several percent due to the neglect of magnification bias, which may lead to a correlation between the shear and the observed number density of lenses. Conclusions. (i) Current semi-analytic models need to be improved in order to match the degree of statistical accuracy expected for future weak-lensing surveys. (ii) Shear B-modes induced by corrections to the first-order approximation are not important for future cosmic-shear surveys. (iii) Magnification bias can be important for galaxy-galaxy-lensing surveys.

The MICE Grand Challenge light-cone simulation – III. Galaxy lensing mocks from all-sky lensing maps

“…The agreement between the Halofit predictions and simulations is within 10% for MICE-IR, and 20% for MICE-GC, down to the resolution scale of the maps used, which corresponds to a multipole = 2× Nside ∼ 16000 17 . The excess of power we find in the MICE-GC convergence maps with respect to the Halofit is in quantitative agreement with a similar analysis (although limited to a small patch of the sky) performed over the Millennium Simulation (see Fig.9 in Hilbert et al (2009)), which has more than one order of magnitude lower particle mass (i.e., ∼ 10 9 M /h).…”

“…The Gaussian approximation is expected to be accurate on large scales and for close to all-sky surveys (see e.g., Cabré et al (2007)), but they tend to underestimate errors on small-scales, where non-linear gravitational growth induce non-Gaussian covariances through the matter trispectrum (Scoccimarro et al 1999;Cooray & Hu 2001). However projection effects inherent to lensing observables mitigate the non-Gaussian contribution relative to the corresponding term in 3D clustering statistics (Semboloni et al 2007;Takada & Jain 2009;Hilbert et al 2009). Given that we only have one single realization in our analysis, the MICE-GC run, we shall stick to the Gaussian approximation for the errors shown in this paper (unless otherwise stated) when comparing to theory predictions, although with the obvious caveat that they tend to underestimate covariances on small-scales.…”

Probing cosmology with weak lensing Minkowski functionals

“…The theoretical predictions for the underlying non-linear matter power are good only to about ∼10% on scales down to ∼ 0.1Mpc [64], which can cause an under-prediction for the convergence power spectrum as well [40,65,66]; the differences are therefore within the accuracy of the theory down to these . …”

Evidence of the accelerated expansion of the Universe from weak lensing tomography with COSMOS

“…The details of the ray-tracing analysis are given in Hilbert et al (2009). In brief, we use tilted lines-of-sight through the simulation to avoid repetition of structures along the backwards lightcone, providing us with 32 quasi-independent 4 deg ×4 deg fields, which we further subdivide into nine COSMOS-like subfields, yielding a total of 288 realizations.…”

“…We find q 0 < 0 at 96.0% confidence using our default priors, or 94.3% confidence for the weaker priors. of Heitmann et al (2010) and Hilbert et al (2009), indicating that models based on Smith et al (2003) slightly underestimate the shear signal, hence a higher σ 8 is required to fit the data. Here we use actual reduced shear estimates from the simulation, but employ shear predictions, as done for the real data (see Sect.…”