Related papers: An Infinite Fractal Cosmos
A geometric spacetime map of the universe is presented, addressing problems inherent in deep space observations and cosmology. Implications for the observer's perspective, the cosmological "horizon" and "flatness" problem, "inflation", and…
We clarify and develop the results of a previous paper on the birth of a closed universe of negative spatial curvature and multiply connected topology. In particular we discuss the initial instanton and the second topology change in more…
The changes of main paradigms on the structure and evolution of the Universe are reviewed. Two puzzles of the modern cosmology, the mean density of matter and the regularity of the Universe on large scales, as well as the possibility to…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
There has been significant recent progress in observational cosmology. This, in turn, has provided an unprecedented picture of the early universe and its evolution. In this review I will present a (biased) view of how one can use these…
This paper explores the fundamental causal limits on how much of the universe we can observe or affect. It distinguishes four principal regions: the affectable universe, the observable universe, the eventually observable universe, and the…
For most of its history, cosmology was a qualitatively constrained discourse on the universe, shaped by limited observational access and the absence of global dynamical laws. This situation has changed decisively in recent decades. Modern…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidus zeta function at infinity, study its properties and…
The evolution of a class of inhomogeneous spherically symmetric universe models possessing a varying cosmological term and a material fluid, with an adiabatic index either constant or not, is studied.
Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the…
This is a brief overview of some turning points in the history of infinitesimals.
We consider the question of properly defining energy and momenta for non asymptotic Minkowskian spaces in general relativity. Only spaces of this type, whose energy, linear 3-momentum, and intrinsic angular momentum vanish, would be…
Cosmology is operating now on a well established and tightly constraining empirical basis. The relativistic LambdaCDM hot big bang theory is consistent with all the present tests; it has become the benchmark. But the many open issues in…
We discuss recent developments related to certain blow up methods suitable for the analysis of cosmological singularities and asymptotics. We review results obtained in a variety of currently popular themes and describe ongoing research…
I present a non-technical and necessarily biased and incomplete overview of our present understanding of the physical universe and its constituents, emphasizing what we have learned from the explosive growth in cosmological and…
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…
Modern cosmological theories invoke the idea that all structure in the Universe originates from quantum fluctuations. Understanding the quantum-to-classical transition for these fluctuations is of central importance not only for the…
The no-boundary proposal provides a compelling theory for the initial conditions of our universe. We study the implications of such initial conditions for ekpyrotic and cyclic cosmologies. These cosmologies allow for the existence of a new…
Evidence for cosmic down-sizing has been growing over the last decade. It is now clear that the major star-forming epoch for the largest galaxies occurred earlier than for smaller galaxies. This not only runs counter to the popular…