相关论文: Geodesics in Open Universes

This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.

We investigate the geodesic motions of a massive particle and light ray in the hyperplane orthogonal to the symmetry axis in the 5-dimensional hypercylindrical spacetime. The class of the solutions depends on one constant a which is the…

The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…

We prove that a proper geodesic metric space has non-positive curvature in the sense of Alexandrov if and only if it satisfies the Euclidean isoperimetric inequality for curves. Our result extends to non-geodesic spaces and non-zero…

The canonical equations of the optical cloaking proposed by Shurig, Pendry and Smith has been proved to be equivalent to the geodesic in a 3-dimensional curved space. Carrying out the argument we extend to the 4-dimensional Riemannian space…

The paper presents results for deriving closed-form analytic solutions of the non-relativistic linear perturbation equations, which govern the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model.…

This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and…

We introduce "anamorphic" cosmology, an approach for explaining the smoothness and flatness of the universe on large scales and the generation of a nearly scale-invariant spectrum of adiabatic density perturbations. The defining feature is…

Inhomogeneous cosmological models are able to fit cosmological observations without dark energy under the assumption that we live close to the "center" of a very large-scale under-dense region. Most studies fitting observations by means of…

Questions such as whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental open problems that high precision modern cosmology needs to resolve. These questions go beyond the scope of…

The universe is nearly isotropic on very large scales. It is much more difficult to show that the universe is radially homogeneous (independent of distance), or equivalently, that it is isotropic about distant points. This taken as an…

Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models. Their unique canonical forms, providing such quantum mechanical observables,…

Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. We have developed a new method for calculating the CMB anisotropy in…

We study the effects of negative spatial curvature on the statistics of inhomogeneities in open cosmological models. In particular we examine the suppression of large-separation correlations in density and gravitational potential…

In this paper, we parametrize the space of isometric immersions of the hyperbolic plane into the hyperbolic 3-space in terms of null-causal curves in the space of oriented geodesics. Moreover, we characterize "ideal cones" (i.e., cones…

This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the…

We propose a method for constructing the specific heat for the universe by following standard definitions of classical thermodynamics, in a spatially flat homogeneous and isotropic spacetime. We use cosmography to represent the specific…

We construct general anisotropic cosmological scenarios governed by an $f(R)=R^n$ gravitational sector. Focusing then on some specific geometries, and modelling the matter content as a perfect fluid, we perform a phase-space analysis. We…

The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is…