相关论文: A new geometrical approach to void statistics

Inhomogeneous universe models have been proposed as an alternative explanation for the apparent acceleration of the cosmic expansion that does not require dark energy. In the simplest class of inhomogeneous models, we live within a large,…

The large-scale distribution of matter in the universe forms a network of clusters, filaments and walls enclosing large empty voids. Voids in turn can be described as a cellular system in which voids/cells define dynamically distinct…

In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that…

Voids in the large scale distribution of galaxies were first recognized and discussed as an astrophysical phenomenon in two papers published in 1978. We published the first (Gregory and Thompson 1978) and Joeveer, Einasto and Tago (1978)…

In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…

Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling…

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…

We explore aspects of the physics of de Sitter (dS) space that are relevant to holography with a positive cosmological constant. First we display a nonlocal map that commutes with the de Sitter isometries, transforms the bulk-boundary…

In this work, major principles of the mathematical constitution of space and the principles of construction of the physical space are presented. Generalized conceptions of distances and dimensionality evaluation are proposed, together with…

The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing…

In this paper, we present a new cosmological model using fractal manifold. We prove that a space defined by this kind of manifold is an expanding space. This model provides us with consistent arguments pertaining to the relationship between…

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though,…

We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter…

Originally proposed by 't Hooft, the brick wall model has recently reemerged as a useful framework for probing quantum aspects of horizon physics, particularly in the context of holography. In this paper, we apply it to asymptotically de…

Quantum field theories on de Sitter spacetime with global U(1) gauge symmetry are deformed using the joint action of the internal symmetry group and a one-parameter group of boosts. The resulting theory turns out to be wedge-local and…

We study the effects of a fixed de Sitter geometry background in scenarios of false vacuum decay. It is currently understood that bubble nucleation processes associated with first order phase transitions are particularly important in…

Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our…

Describing dynamics in a gravitational universe with positive cosmological constant, such as de Sitter space, is a conceptually challenging problem. We propose a principle for constructing a quantum system that can potentially be used to…

These lectures deal with our current knowledge of the matter distribution in the universe, focusing on how this is studied via the large-scale structure seen in galaxy surveys. We first assemble the necessary basics needed to understand the…

We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…