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Observational constraints guide one forcefully to examine models in which the matter density is substantially less than critical density. Particularly noteworthy are those which are consistent with inflation. For these models, microwave…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
Inhomogeneous cosmological models such as the Stephani universes could, in principle, provide an explanation for the observed accelerated expansion of the Universe. Working with a concrete, popular model of the Stephani cosmology -- the…
Cosmic voids - the low density regions in the Universe - as characteristic features of the large scale matter distribution, are known for their hyperbolic properties. The latter implies the deviation of photon beams due to their…
Astrophysical observations indicate that the ``Local Universe" has a relatively lower matter density ($\Omega_0$) than the predictions of the standard inflation cosmology and the large-scale motions of galaxies which provide a mean mass…
If the spatial section of the universe is multiply connected, repeated images or patterns are expected to be detected observationally. However, due to the finite distance to the last scattering surface, such pattern repetitions could be…
Modern astronomical observations in cosmology provide increasingly strong evidence that the expansion of the Universe is accelerating. Explanations of the cosmic acceleration within the framework of general relativity use the hypothesis…
We challenge the widely held belief that the cosmological principle is an obvious consequence of the observed isotropy of the cosmic microwave background radiation, combined with the Copernican principle. We perform a detailed analysis of a…
It is very difficult to obtain a realistic model of a closed inflationary universe. Even if one fine-tunes the total number of e-folds to be sufficiently small, the resulting universe typically has large density perturbations on the scale…
The matter content of the Universe is strongly inhomogeneous on small scales. Motivated by this fact, we consider a model of the Universe that has regularly spaced discrete masses, rather than a continuous fluid. The optical properties of…
We study conditions for the existence of asymptotic observables in cosmology. With the exception of de Sitter space, the thermal properties of accelerating universes permit arbitrarily long observations, and guarantee the production of…
In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and…
Thanks to new technology of observations and fresh inputs from particle physics, cosmology has advanced on both observational and theoretical fronts. It is therefore opportune that we take stock of the cosmological situation today and…
Quantum cosmology in the presence of a fundamental minimal length is analyzed in the context of the flat isotropic and the Taub cosmological models. Such minimal scale comes out from a generalized uncertainty principle and the quantization…
Voids are dominant features of the cosmic web. We revisit the cosmological information content of voids and connect void properties with the parameters of the background universe. We combine analytical results with a suite of large n-body…
At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking `no-boundary' wavefunction, in contrast to the suppression at small universes for the…
The observable universe is fundamentally inhomogeneous and anisotropic. Quantum description of the generation of these inhomogeneities and anisotropies is ill-understood and unsatisfactory. After providing a brief account of the standard…
In the era of precision cosmology, even percentage level effects are significant on cosmological observables. The recent tension between the local and global values of $H_0$ is much more significant than this, and any possible solution…
In the simplest cosmological models consistent with General Relativity, the total volume of the Universe is either finite or infinite, depending on whether or not the spatial curvature is positive. Current data suggest that the curvature is…
Although the cubic T^3 "small universe" has been ruled out by COBE/DMR results as an interesting cosmological model, we still have the possibility of living in a universe with a more anisotropic topology such as a rectangular T^3 "small…