## Simulating weak gravitational lensing for cosmology

##### Abstract

This thesis will present a new cosmic shear analysis pipeline SUNGLASS (Simulated
UNiverses for Gravitational Lensing Analysis and Shear Surveys). SUNGLASS is
a pipeline that rapidly generates simulated universes for weak lensing and cosmic
shear analysis. The pipeline forms suites of cosmological N-body simulations and
performs tomographic cosmic shear analysis using a novel line-of-sight integration
through the simulations while saving the particle lightcone information. Galaxy
shear and convergence catalogues with realistic 3-D galaxy redshift distributions are
produced for the purposes of testing weak lensing analysis techniques and generating
covariance matrices for data analysis and cosmological parameter estimation. This
thesis presents a suite of fast medium-resolution simulations with shear and convergence maps for a generic 100 square degree survey out to a redshift of z = 1.5, with
angular power spectra agreeing with the theoretical expectations to better than a
few percent accuracy up to ℓ = 103 for all source redshifts up to z = 1.5 and
wavenumbers up to ℓ = 2000 for source redshifts z ≥ 1.1. A two-parameter Gaussian likelihood analysis of Ωm and σ8 is also performed on the suite of simulations
for a 2-D weak lensing survey, demonstrating that the cosmological parameters are
recovered from the simulations and the covariance matrices are stable for data analysis, with negligible bias.
An investigation into the accuracy of traditional Fisher matrix calculations is presented. Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach
usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra
covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe,
non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information
will change the predictions of cosmological parameter accuracy. In this thesis, the
loss of information is quantified by comparing näıve Gaussian Fisher matrix forecasts
with a Maximum Likelihood parameter estimation analysis of the suite of mock weak
lensing catalogues derived from the SUNGLASS pipeline, for 2-D and tomographic
shear analyses of a Euclid-like survey. In both cases the 68% confidence area of the Ωm − σ8 plane is found to increase by a factor 5. However, the marginal errors increase by just 20 to 40%. A new method is proposed to model the effects of non-linear
shear-power mode-coupling in the Fisher Matrix by approximating the shear-power
distribution as a multivariate Gaussian with a covariance matrix derived from the
mock weak lensing survey. The findings in this thesis show that this approximation
can reproduce the 68% confidence regions of the full Maximum Likelihood analysis
in the Ωm − σ8 plane to high accuracy for both 2-D and tomographic weak lensing
surveys. Finally, three multi-parameter analyses of (Ωm, σ8, ns), (Ωm, σ8, ns,
ΩΛ)and (Ωm, σ8, h, ns, w0, wa) are performed to compare the Gaussian and non-linear
mode-coupled Fisher matrix contours. The multi-parameter volumes of the 1σ error contours for the six-parameter non-linear Fisher analysis are consistently larger
than for the Gaussian case, and the shape of the 68% confidence volume is modified.
These results strongly suggest that future Fisher Matrix estimates of cosmological
parameter accuracies should include mode-coupling effects.