Related papers: Minkowski Functionals in Cosmology: An Overview
The past few years have seen several breakthroughs in particle astrophysics and cosmology. In several cases, new observations can only be explained with the introduction of new fundamental physics. In this talk I summarize some of these…
The Minkowski question mark function is a rich object which can be explored from the perspective of dynamical systems, complex dynamics, metric number theory, multifractal analysis, transfer operators, integral transforms, and as a function…
This paper gives a brief overview of some new work in number theory and algebra, and also studies the arithmetic and algebraic properties of Minkowski balls and spheres. The content of the paper is presented in more detail in the table of…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
A comparison of the standard models in particle physics and in cosmology demonstrates that they are not compatible, though both are well established. Basics of modern cosmology are briefly reviewed. It is argued that the measurements of the…
The dramatic confrontation between new observations and theories of the early and recent universe makes cosmology one of the most rapidly advancing fields in the physical sciences. The universe is a unique laboratory in which to probe…
The complex Minkowski phase space has the physical interpretation of the phase space of the scalar massive conformal particle. The aim of the paper is the construction and investigation of the quantum complex Minkowski space.
An introduction to various topics in neutrino astrophysics is given for students with little prior exposure to this field. We explain neutrino production and propagation in stars, neutrino oscillations, and experimental searches for this…
A new method is presented for assigning distributional curvature, in an invariant manner, to a space-time of low differentiability, using the techniques of Colombeau's `new generalised functions'. The method is applied to show that…
Understanding the behavior of the universe at large depends critically on insights about the smallest units of matter and their fundamental interactions. Inflationary cosmology is a highly successful framework for exploring these…
These lectures were addressed to nonspecialists willing to learn some basic facts, approaches, tools and observational evidence which conform modern cosmology. The aim is also to try to complement the many excellent treatises that exists on…
Recently, a new field of study called fractional cosmology has emerged. It uses fractional calculus to modify the standard derivative equations and change the Friedmann equations. The evolution of cosmic species densities is also affected…
We consider the cosmological application of a (variant of) relatively newly proposed model \cite{1609.06915} unifying inflation, dark energy, dark matter, and the Higgs mechanism. The model was originally defined using additional…
I discuss some aspects of the use of computers in Relativity, Astrophysics and Cosmology. For each section I provide two examples representative of the field, including gravitational collapse, black hole imagery, supernovae explosions,…
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
The last 20 years have seen an explosion in our understanding of the large-scale distribution and motions of galaxies in the nearby universe. The field has moved from a largely qualitative, morphological description of the structures seen…
We review cosmological relativity, a new special theory of relativity that was recently developed for cosmology, and discuss in detail some of its aspects.
After exactly a century since the formulation of the general theory of relativity, the phenomenon of gravitational lensing is still an extremely powerful method for investigating in astrophysics and cosmology. Indeed, it is adopted to study…