## Weak gravitational lensing in the cosmic microwave background : reconstructing the lensing convergence.

##### Abstract

Many of the most significant constraints on the standard model of Cosmology describing the
origins, contents and evolution of the Universe arise from the Cosmic Microwave Background
(CMB). As we enter an era of precision cosmology, with more sensitive and higher angular resolution
ground, balloon and space-based experiments, it is becoming increasingly important to
understand the small-scale secondary anisotropies of the CMB. One of the most important of
these secondary anisotropies comes from weak gravitational lensing, whereby free-streaming
CMB photons are deflected by the gravitational potentials in the large-scale structure of the Universe.
This has several important effects including modifications to the CMB power spectrum,
the introduction of non-Gaussianities and the generation of B-mode polarization. In principle it
is possible to reconstruct the the projection of the gravitational potential on the celestial sphere
directly from observations of the CMB temperature anisotropies by examining the distinctive
non-Gaussian signature the gravitational lensing imparts on to the CMB. This reconstructed map
can be used to constrain the amplitude of the mass fluctuations in the early Universe and contains
significant information regarding the dark matter distribution throughout the Universe.
After a review of the standard Big Bang cosmological model the phenomenon of gravitational
lensing is introduced. Equations for the deflection angle and lensing convergence are derived, as
well as their power spectra, and the effect that gravitational lensing has on the CMB is discussed.
In the main part of the thesis we study two methods for reconstructing the lensing convergence,
the standard harmonic space quadratic estimator and a second estimator which is defined in real
space. Each of the estimators is derived and implemented to recover reconstructed lensing convergence
maps. The various biases that are inherent in the estimators is discussed, including
details of how these biases can be removed. The performance of each of the estimators in reconstructing
the lensing convergence is evaluated and contrasted.
The final part of this thesis involves an analysis of a non-linear bias which affects both the harii
monic space and real space estimators, resulting from a break down of the linear approximation,
which arises if the lensing field has a sufficiently large magnitude. The effect of the non-linear
bias on the reconstructed lensing field is evaluated, and comparison of these results with the
reconstructed lensing amplitude from the Atacama Cosmology Telescope (ACT) and the South
Pole Telescope (SPT) lensing measurement provides an estimate for the level of importance of
the non-linear bias.