Abstract
The primordial CMB anisotropies generated at the last scattering surface are distorted by late time effects as the path of the CMB photons is perturbed by the intervening spacetime. One of these, weak gravitational lensing, is caused by transverse deflections to the photon trajectories by the mass overdensities of the large-scale structure of the universe. The effect on the CMB anisotropies is usually calculated with a remapping approach where higher order anisotropies are reconstructed from solutions to the per-turbed geodesic equation. In this thesis we study an alternative approach: solving the Boltzmann equation directly. This allows one to see explicitly which physical effects are involved, how they couple with weak lensing, and what assumptions must be made to derive the remapping approach. We review in detail how both the geodesic equation and the Boltzmann equation can be used to derive the weak lensing effect. By comparing the two methods we make the approximations made in the standard geodesic equation approach explicit and contrast them with those of the Boltzmann equation method. We use both methods to calculate the effect of weak lensing on the CMB anisotropies up to fourth order and then prove their equivalence up to fourth order.In second order calculations of the weak lensing effect the “Born approximation” is used: integrals are evaluated along the unperturbed photon path. In previous work it has been argued that extending the remapping approach to higher orders necessitates relaxing the Born approximation, resulting in terms that are due to “post-Born” physical effects. By comparing equivalent results derived using the two methods, and making use of diagrams that track the coupling of sources and lenses at different points in spacetime, we clarify the physical interpretation of the results and show that these “post-Born” effects of weak lensing at fourth order are in fact equivalent to lens-lens couplings in the Born approximation.
Date of Award | 1 Jun 2022 |
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Original language | English |
Awarding Institution |
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Supervisor | Eugene Lim (Supervisor) & Mairi Sakellariadou (Supervisor) |