Related papers: Closed Spaces in Cosmology
We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer…
In complex general relativity, Lorentzian space-time is replaced by a four-complex-dimensional complex-Riemannian manifold, with holomorphic connection and holomorphic curvature tensor. A multisymplectic analysis shows that the Hamiltonian…
In this manuscript, we aim to classify and characterize the moduli space of homogeneous spin connections and homogeneous SU(2) connections on three-dimensional Riemannian homogeneous spaces. An analysis of the topology of the associated…
We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop…
Observational evidence, together with practical computations and modeling, supports a Euclidean spatial sector in the current cosmological model based on the FLRW metric. This, however, would imply that the total amount of matter and energy…
We argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar…
Background boucing cosmologies in the framework of General Relativity, driven by a single scalar field filling the Universe, and with a quasi-matter domination period, i.e., depicting the so-called Matter Bounce Scenario, are reconstructed…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
This thesis investigates how the metric and tetrad formulations of three gravitational field theories in manifolds with timelike boundaries within the covariant phase space program. With the recently developed relative bicomplex framework,…
Spherical manifolds yield cosmic spaces with positive curvature. They result by closing pieces from the sphere used by Einstein for his initial cosmology. Harmonic analysis on the manifolds aims at explaining the observed low amplitudes at…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-component perfect-fluid and minimally coupled scalar field is considered. When the pressures in all spaces are proportional to the density, the…
Averaged inhomogeneous cosmologies lie at the forefront of interest, since cosmological parameters like the rate of expansion or the mass density are to be considered as volume-averaged quantities and only these can be compared with…
Certain closed-universe big-bang/big-crunch cosmological spacetimes may be obtained by analytic continuation from asymptotically AdS Euclidean wormholes, as emphasized by Maldacena and Maoz. We investigate how these Euclidean wormhole…
Some properties of Riemannian foliations on closed manifolds are generalized to compact equicontinuous foliated spaces. For instance, it is proved that all holonomy covers of the leaves are quasi-isometric to each other.
We introduce the totally absolute lightcone curvature for a spacelike submanifold with general codimension and investigate global properties of this curvature. One of the consequences is that the Chern-Lashof type inequality holds. Then the…
We show that in Lorentzian manifolds, sectional curvature bounds of the form $\mathcal{R}\le K\,$, as defined by Andersson and Howard, are closely tied to space-time convex and $\lambda$-convex ($\lambda>0$) functions, as defined by Gibbons…
We prove that various spaces of constrained positive scalar curvature metrics on compact 3-manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean…
We provide intrinsic conditions on the geometry of horospheres in a closed, negatively curved Riemannian manifold of dimension greater than or equal to 3, which guarantee that the sectional curvature is constant.
Studying spacetimes with continuous symmetries by dimensional reduction to a lower dimensional spacetime is a well known technique in field theory and gravity. Recently, its use has been advocated in numerical relativity as an efficient…