相关论文: A new geometrical approach to void statistics
Decaying vacuum cosmological models evolving smoothly between two extreme (very early and late time) de Sitter phases are capable to solve or at least to alleviate some cosmological puzzles, among them: (i) the singularity, (ii) horizon,…
A method for detecting voids in the galaxy distribution is presented. Using this method, we have identified 732 voids with a radius of the seed sphere Rseed > 4.0h^{-1}Mpc in a volume-limited sample of galaxies from the southern part of the…
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…
Two new quantum anti-de Sitter so(4,2) and de Sitter so(5,1) algebras are presented. These deformations are called either time-type or space-type according to the dimensional properties of the deformation parameter. Their Hopf structure,…
We consider new cosmological solutions which generalize the cosmological patch of the Anti-de Sitter (AdS) space-time, allowing for fluids with equations of state such that $w\neq -1$. We use them to derive the associated full manifolds. We…
Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…
We calculate the total gravitational energy and the gravitational energy density of the de Sitter space using the definition of localized energy that arises in the framework of the teleparallel equivalent of general relativity. We find that…
In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some…
de Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss…
We use analytic estimates and numerical simulations to explore the stochastic approach to vacuum decay. According to this approach, the time derivative of a scalar field, which is in a local vacuum state, develops a large fluctuation and…
In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure"…
Recent observations in cosmology indicate an accelerating expansion of the universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic…
The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability properties is reviewed. The constant Gaussian curvature of the…
A signature of the dark energy equation of state may be observed in the shape of voids. We estimate the constraints on cosmological parameters that would be determined from the ellipticity distribution of voids from future spectroscopic…
Cosmic voids are increasingly recognized as a promising tool for cosmological exploration. Their distribution and density profiles are highly responsive to alterations in gravitational theories, along with the influences of dark energy and…
I discuss empty space, as it appears in the physical foundations of relativistic field theories and in the semiclassical study of isolated systems. Of particular interest is the relationship between empirical measurements of the…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
Cosmic voids identified in the spatial distribution of galaxies provide complementary information to two-point statistics. In particular, constraints on the neutrino mass sum, $\sum m_\nu$, promise to benefit from the inclusion of void…