Related papers: Flat Universe with Hyperbolic Voids
This study examines the gravitational and thermodynamic properties of static, spherically symmetric black holes within cosmic voids -- vast underdense regions of the universe. By deriving a novel solution based on a universal density…
We build a simple cosmological model by means of a parabolic Lema\^{i}tre-Tolman-Bondi (LTB) metric up to a redshift $z\simeq 0.4$, an hyperbolic Friedmann metric for $z\sim 0.4$ up to the scale where dimming galaxies are observed ($z\sim…
Applying the first law of thermodynamics to the apparent horizon of a Friedmann-Robertson-Walker universe and assuming the geometric entropy given by a quarter of the apparent horizon area, we derive the Friedmann equations describing the…
Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an…
Recent work by the authors led to the development of a mathematical theory dealing with `second--order hyperbolic Fuchsian systems', as we call them. In the present paper, we adopt a physical standpoint and discuss the implications of this…
We investigate the cosmological implications of $f(Q)$ gravity, which is a modified theory of gravity based on non-metricity, in non-flat geometry. We perform a detailed dynamical-system analysis keeping the $f(Q)$ function completely…
The talk is devoted to the "extended phase space" approach to Quantum Geometrodynamics. The premises that have led to the formulation of this approach are briefly reviewed, namely, non-trivial topology of the Universe which implies the…
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales. We show that some such results remain valid for metric spaces with non-unique…
Gravity is a macroscopic manifestation of a microscopic quantum theory of space-time, just as the theories of elasticity and hydrodynamics are the macroscopic manifestation of the underlying quantum theory of atoms. The connection of…
Currently, a large amount of data implies that the matter constituents of the cosmological dark sector might be collisional. An attractive feature of such a possibility is that, it can reconcile dark matter (DM) and dark energy (DE) in…
The Hawking energy has a monotonicity property under the inverse mean curvature flow on totally umbilic hypersurfaces with constant scalar curvature in Einstein spaces. It grows if the hypersurface is spacelike, and decreases if it is…
We discuss some aspects of cosmology in metric-affine theories of gravity where metric and affine connection are independent variables. Such constructions, apart from the usual energy-momentum tensor, have an additional source, that of…
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact…
In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which…
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are…
A cosmological model with perfect fluid and self-interacting quintessence field is considered in the framework of the spatially flat Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical quantities depend on the volume…
We consider a Jordan domain diffeomorphic to a closed two-dimensional disk with a smooth boundary. Assuming the Gauss curvature of the domain has a negative lower bound, the Gauss-Bonnet formula provides an upper bound for the total…
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. For compact topologies, the two main effects on the CMB are: (1) the…
The emergence of a highly improbable coincidence in cosmological observations speaks to a remarkably simple cosmic expansion. Compelling evidence now suggests that the Universe's gravitational horizon, coincident with the better known…
In the context of effective Friedmann equation we classify the cosmologies in multi-scalar models with an arbitrary scalar potential $V$ according to their geometric properties. It is shown that all flat cosmologies are geodesics with…