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We present a new algorithm that can reconstruct the full distributions of metric components within the class of spherically symmetric dust universes that may include a cosmological constant. The algorithm is capable of confronting this class of solutions with arbitrary data and opens a new observational window to determine the value of the cosmological constant. In this work we use luminosity and age data to constrain the geometry of the universe up to a redshift of $z = 1.75$. We show that, although current data are perfectly compatible with homogeneous models of the universe, simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time universe cannot yet be ruled out. In doing so we reconstruct the density of cold dark matter out to $z = 1.75$ and derive constraints on the metric components when the universe was 10.5 Gyr old within a comoving volume of approximately 1 Gpc$^{3}$.
In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations --- the so-called circles-in-the-sky. Searches undertaken for nearly ant
The last century has seen enormous progress in our understanding of the Universe. We know the life cycles of stars, the structure of galaxies, the remnants of the big bang, and have a general understanding of how the Universe evolved. We have come re
The aim of this thesis is to question some of the basic assumptions that go into building the $Lambda$CDM model of our universe. The assumptions we focus on are the initial conditions of the universe, the fundamental forces in the universe on large s
The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we inter
In the standard big bang model the universe starts in a radiation dominated era, where the gravitational perturbations are described by second order differential equations, which will generally have two orthogonal set of solutions. One is the so call