Related papers: A Class of Cosmological Matrix Models
Cardassian models are an alternative to general relativity which have been proposed as an approach to explaining accelerated cosmic expansion while avoiding directly introducing dark energy. They are generally formulated only in the…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.
In these Lectures, I review various extensions of the Lambda-Cold Dark Matter model, characterized by additional light degrees of freedom in the dark sector. In order to reproduce the successful phenomenology of GR in the solar system,…
There are several ways to generalize characteristic classes for singular algebraic varieties. The simplest ones to describe are Chern-Mather classes obtained by Nash blow up. They serve as an ingredient to construct…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…
We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of…
In this work, we consider the cosmological constraints on the interacting dark energy models. We generalize the models considered previously by Guo {\it et al.}, Costa and Alcaniz, and try to discuss two general types of models: type I…
Advantages of inhomogeneous cosmological models that are exact solutions of Einstein's equations over linearised perturbations of homogeneous models are presented. Examples of effects that can be described in the inhomogeneous ones are…
New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial…
In this talk I review the present status of inflationary cosmology and its emergence as the basic paradigm behind the Standard Cosmological Model, with parameters determined today at better than 10% level from CMB and LSS observations.
We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and…
We show that the model of discrete spaces that we have proposed in previous contributions gives a comprehensive and detailed interpretation of the properties of the standard model of particles. Moreover the model also suggests the possible…
We briefly summarize the idea of cosmological models with compact, flat spatial sections. It has been suggested that, because of the COBE satellite's maps of the microwave background, such models cannot be small in the sense of Ellis, and…
Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…
We consider a new matrix model based on the simply connected compact exceptional Lie group E6. A matrix Chern-Simons theory is directly derived from the invariant on E6. It is stated that the similar argument as Smolin which derives an…
We investigate the dynamical features of a large family of running vacuum cosmologies for which $\Lambda$ evolves as a polynomial in the Hubble parameter. Specifically, using the critical point analysis we study the existence and the…
We argue that more cosmological solutions in massive gravity can be obtained if the metric tensor and the tensor $\Sigma_{\mu\nu}$ defined by St\"{u}ckelberg fields take the homogeneous and isotropic form. The standard cosmology with matter…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved)…