### Weak Gravitational Lensing Uncertainties

### Tingting Lu

Doctor of Philosophy 2009

Graduate Department of Astronomy and Astrophysics, University of Toronto
Dark matter dominates the mass distribution of the universe, and dark
energy determines its expansion. The two are the most mysterious and
attractive subjects in modern cosmology, because they provide an
opportunity to discover new fundamental physics.

Cosmological weak gravitational lensing, which describes the
deflection of photons by the gravitational force from large-scale
structure in the universe, has been an active area of research in the
past decade with many completed, ongoing, and upcoming surveys.
Because weak lensing is sensitive to the growth of structure and
expansion history of the universe, it is a great tool for improving
our understanding of both dark matter and dark energy problems.

Cosmic structures have become non-linear by gravitational
clustering. The non-linear structures are important to weak lensing,
and cause non-Gaussianity in the lensing maps. In this thesis, I
study the influence of non-linearity and non-Gaussianity on the
uncertainty of lensing measurements. I develop a new method to
robustly measure the covariance matrix of the lensing convergence
power spectrum, from simulations. Because 21-cm intensity map may soon
cover half sky at redshift 1-4, I build optimal estimators for
reconstructing lensing from the 21-cm sources. I develop Gaussian
optimal estimators which can be derived analytically, and non-Gaussian
optimal estimators which can be constructed numerically from
simulation data. I then run a large number of N-body simulations. For
both lenses and 21-cm sources, I explore the statistical uncertainties
in ii the simulation data.

We show that the non-Gaussianity nature of lensing decreases the dark
energy figure of merit by a factor of 1.3 to 1.6 for a few future
surveys. We also find that the non-Gaussianity nature of the 21-cm
sources reduces the signal to noise ratio by several orders of
magnitude. The reconstruction noise saturates at mildly non-linear
scales, where the linear power spectrum of the source is
Delta^2 ~ 0.2 - 0.5. For 21-cm sources at z ~ 2-4, the
lensing reconstruction is limited by cosmic variance at ell <~ 100, which
is in the linear regime of gravitational growth, and robustly
predicted by theory. This allows promising constraints to various
modified gravity and dark energy models.