Ray tracing & averaging in Szekeres cosmological models. (2022)
In this thesis, we perform ray tracing analyses of the COMPOSITE dataset of 4534 galaxy redshifts and distances using quasi-spherical Szekeres models. The Szekeres models are a class of exact inhomogeneous dust solutions of the Einstein equations, which we utilise as toy models of local inhomogeneous structures for distances ≲ 150 h⁻¹ Mpc. In our case, we choose specific models that asymptote to the FLRW model beyond ≃ 100 h⁻¹ Mpc, to restrict attention to the effects of ‘local structure’. These solutions allow us to simulate light propagation through a local under-dense void with an adjacent over-dense structure, as measured by an observer situated at different points within the structures of the model. By ray tracing null geodesics over the sky of this observer while performing radial and angular averages, we have attempted to constrain the Szekeres models to match the Hubble expansion anisotropy of the COMPOSITE dataset, as well as the dipole and quadrupole anisotropies of the Cosmic Microwave Background (CMB). Previous ray tracing investigations undertaken by Bolejko et al.  have indicated potential non-kinematic contributions to the CMB dipole anisotropy due to relativistic differential expansion on the scale of local inhomogeneities. We revisit these results with corrections applied to a bug in their null vector initialisation procedure that led to some incorrect conclusions. We find that the application of Haantjes transformations to their Szekeres model is a promising avenue for obtaining a full match to the Hubble expansion anisotropy present in the COMPOSITE dataset.
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