Related papers: A Class of Cosmological Matrix Models
At present, there is practically no doubt that general relativity is closely related to gravity. Moreover, after the work of Jacobson, Padmanabhan and others, it became clear that a thermodynamic interpretation of Einstein's relativistic…
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of…
We review a proposal to obtain an emergent metric space-time and an emergent early universe cosmology from the BFSS matrix model. Some challenges and directions for future research are outlined.
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
We comment on the necessity of a unified approximative scheme within relativistic cosmology which would allow us to classify different cosmological models in a systematic way. We also report on recent progresses in formulating a…
In this paper we analyse the possibility of constructing singularity-free inhomogeneous cosmological models with a pure radiation field as matter content. It is shown that the conditions for regularity are very easy to implement and…
The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations…
We discuss some aspects of recent research as well as more general issues about motivation, useful methods and open problems in the field of cosmological singularities. In particular, we review some of the approaches to the general area and…
In this expository article we describe the attempt of defining cosmological singularities and we discuss their meaning in classical and quantum cosmology.
We present a new class of exact homogeneous cosmological solutions with a radiation fluid for all scalar-tensor theories. The solutions belong to Bianchi type $VI_{h}$ cosmologies. Explicit examples of nonsingular homogeneous scalar-tensor…
The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon…
We consider cosmological models in scalar tensor theories of gravity that describe an accelerating universe, and we study a family of inverse power law potentials, for which exact solutions of the Einstein equations are known. We also…
This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…
In recent years, by theory and observation cosmology has advanced substantially. Parameters of the concordance or $\Lambda$CDM cosmological model are given with unprecedented precision ("precision cosmology"). On the other side, 95% of the…
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…
In these notes we present a selection of topics, each section approximately amounting to one lecture. We begin with a brief recapitulation of General Relativity, and the Standard Model of Cosmology. This is followed by lectures on important…
We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can…
By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing…
We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…