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Recent observations suggest that a large fraction of the energy density of the universe has negative pressure. One explanation is vacuum energy density; another is quintessence in the form of a scalar field slowly evolving down a potential.…
The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply connected on scales smaller than the particle…
An introduction to modern theories for the origin of structure in the Universe is given. After a brief review of the growth of cosmological perturbations in an expanding Universe and a summary of some important observational results, the…
In inflation cosmologies, cosmic structure develops through the gravitational instability of the inevitable quantum noise in primordial scalar fields. I show how the acceleration of the universe defines the shape of the primordial spectrum…
A new phenomenological dark energy model, originally associated to the large-scale structure formation and considered as a solution to the fine-tuning and coincidence problems related to the cosmological constant, was analyzed within the…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
As evidenced by a great number of works, it is common practice to assume that the Universe is flat. However, the majority of studies which make use of observational data to constrain the curvature density parameter are premised on the…
A brief account is given of large-scale structure modelling based on the assumption that the initial perturbations arise from inflation. A recap is made of the implications of inflation for large-scale structure; under the widely applicable…
Precision measurements of anisotropies in the cosmic microwave background and of the clustering of large-scale structure have supposedly confirmed that the primordial density perturbation has a (nearly) scale-invariant spectrum. However…
We study the cosmology with the running dark energy. The parametrization of dark energy with the respect to the redshift is derived from the first principles of quantum mechanics. Energy density of dark energy is obtained from the quantum…
We analyze the evolution of energy density fluctuations in cosmological scenarios with a mixture of cold dark matter and quintessence, in which the quintessence field is modeled by a constant equation of state. We obtain analytic…
We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear…
Elucidating the interplay of defect and stress at the microscopic level is a fundamental physical problem that has strong connection with materials science. Here, based on the two-dimensional crystal model, we show that the instability mode…
For general number of spatial dimensions we investigate the cosmological dynamics driven by a cosmological constant and by a source with barotropic equation of state. It is assumed that for both those sources the energy density can be…
Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution…
We investigate the cosmological consequences of a simple theory in which the electric charge $e$ is allowed to vary. The theory is locally gauge and Lorentz invariant, and satisfies general covariance. We find that in this theory the fine…
We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark…
Using a number of numerical tests and analytic arguments we investigate how measurements of cosmic shear lead to constraints on dark energy. We find that, in contrast to the case with galaxy number density correlation functions, standard…
We discuss a model of the universe where dark energy is replaced by electrically-charged extremely-massive dark matter. The cosmological constant has a value of the same order as the mean matter density, consistent with observations, and is…
The local Universe displays a rich hierarchical pattern of galaxy clusters and superclusters. The early Universe, however, was almost smooth, with only slight 'ripples' seen in the cosmic microwave background radiation. Models of the…