IDEAL characterizes FLRW spacetimes with scalar fields.
problem Characterize FLRW spacetimes with scalar fields.
method IDEAL (Intrinsic, Deductive, Explicit, Algorithmic) characterization of spacetime metrics.
result First IDEAL characterization of cosmological FLRW spacetimes with and without a dynamical scalar field.
The paper examines isotropic cosmological space-times with changing sectional curvature.
problem Cosmological space-times with changing sectional curvature.
method Analysis of a family of geometrically well-behaved cosmological space-times foliated by isotropic hypersurfaces.
result Only space-time isometries ensure the rigidity properties of isotropic cosmological space-times.
Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.
problem Future stability of expanding FLRW solutions with spatial topology R^3.
method Nonlinear stability analysis of spherically symmetric perturbations.
result Decay rates of energy momentum tensor components compared to Minkowski space.
The paper proves that certain FLRW spacetimes cannot be extended past the big bang.
problem The singularity structure of FLRW spacetimes without particle horizons at the C0-level. method Analyzing the singularity structure of FLRW spacetimes with constant spatial curvature.
result A geometric obstruction prevents continuous spacetime extensions for a wide range of scale factors in the case of K=−1. The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity. In previous papers it has been proposed an equivalent form of Einstein's equation, which extends i…
Defines conformal reference frames for Lorentzian manifolds.
problem Understanding causal relations in cosmology.
method Projection of six-dimensional sky bundle to three-dimensional manifold, celestial transform, contact structure.
result Explicit expression of a 1-form generating contact structure and equation for flow of time.
New findings show cosmological constant as initial condition for non-isotropic spacetimes.
problem Cosmological constant as initial condition in non-isotropic spacetimes.
method Generalized previous results to non-isotropic spacetimes.
result Quasi de Sitter expansion for early universe, potential for inflationary scenarios.
Study examines C0-inextendibility of spacetimes, focusing on FLRW models.
problem Examining the extendibility of spacetimes, particularly focusing on FLRW models.
method Reviewing Sbierski's methodology and applying similar techniques to new observations.
result Certain open FLRW spacetimes admit C0 extensions through the big bang. The study explores spacetimes with changing spatial curvature, leading to topological transitions.
problem The need for a model that avoids infinite matter and energy after the Big Bang.
method Investigates spacetimes with time-dependent spatial curvature, allowing it to change sign.
result Topological transitions are possible in spacetimes with time-dependent spatial curvature.
New cosmological spacetimes without CMC Cauchy surfaces found.
problem Finding CMC Cauchy surfaces in cosmological spacetimes.
method Generalized Bartnik's construction to connected sums of three-manifolds.
result Cosmological spacetimes without CMC Cauchy surfaces for any compact three-manifolds.
Milne-like spacetimes offer solutions to cosmological problems.
problem Inconsistency with classical cosmology and radiation era.
method Analyzing FLRW models and spacetime extensions.
result Milne-like spacetimes are consistent with inflationary theory.
The paper proves stability of certain cosmological models with negative spatial curvature.
problem Stability of Friedmann-Lemaître-Robertson-Walker cosmological models with negative spatial curvature.
method Linear stability analysis using Hodge decomposition and energy estimates.
result Uniform boundedness and decay of solutions to the linearized Einstein-Euler system.
The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.
problem Investigating the past inextendibility of FLRW spacetimes.
method Using the volume-distance-ratio (VDR) asymptote to assess spacetime inextendibility criteria.
result Conditions for past inextendibility of FLRW spacetimes are identified.
New proof shows FLRW spacetimes can't be extended smoothly in certain axisymmetric cases.
problem Proving smooth extension of FLRW spacetimes in specific spacetime classes.
method Extending previous work on spherically symmetric spacetimes to axisymmetric spacetimes.
result Demonstrates C0-inextendibility for FLRW spacetimes in a subclass of axisymmetric spacetimes. Proves some flat spacetimes can't be extended smoothly.
problem Proving smooth extension of certain FLRW spacetimes.
method Utilizing Sbierski's C0-inextendibility techniques. result Proves C0-inextendibility of spatially flat FLRW spacetimes. The paper simplifies FLRW photon propagators using geometric embeddings.
problem Understanding Friedmann-Lemaître-Robertson-Walker (FLRW) spaces.
method Differential-geometric methods applied to FLRW spaces as submanifolds in \(\mathbb{R}^{n+2}\).
result New and simplified expressions for the photon propagator in four dimensions.
New approach classifies conformal Killing vector fields for FLRW space-time.
problem Classifying conformal Killing vector fields for FLRW space-time.
method Introduced new perspective on conformal Killing vector fields for FLRW space-time, considering three cases for the conformal factor.
result Nine conformal vector fields on FLRW, six of which are Killing and the rest non-Killing.
New cosmological models with changing curvature slices.
problem Cosmological models with varying and sign-changing curvature.
method Constructing globally hyperbolic spacetimes with slices of constant curvature that can change sign.
result Shows at least one comoving observer disappearing in finite time.
Study on future stability of FLRW spacetime solutions with decelerated expansion.
problem Stability of solutions to Einstein equations coupled with a nonlinear scalar field.
method Decomposition of metric and scalar field perturbations into spatial averages and oscillatory remainders.
result Future-stability of FLRW spacetime solutions for 1/3<p<1. In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf …
New method splits Einstein field equations for general spacetime threading.
problem Solving Einstein field equations in complex spacetime geometries.
method General (1+3) threading approach to split EFE and conservation laws.
result Perturbation Friedman equations derived in almost FLRW universe.
Study of generalized cones in Lorentzian geometry with causality and curvature analysis.
problem Understanding causality and curvature in Lorentzian warped products.
method Analyzing generalized cones as Lorentzian length spaces with explicit descriptions and metric curvature bounds.
result Prove singularity theorems for non-positive lower timelike curvature bounds.
The paper examines gravitational singularities in spacetimes and proves inextendibility.
problem Investigating gravitational singularities in spacetimes.
method Analyzing local holonomy and using it to prove inextendibility.
result Proves the Cloc0,1-inextendibility of certain spacetimes. Exploring distance functions on spacetime models.
problem No canonical distance function exists for Lorentzian manifolds.
method Comparing Riemannianization and null distance function approaches.
result Concrete comparison of distance functions in GRW setting.
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimens…
Bayesian Neural Networks improve precision cosmology from simulations.
problem Extracting precise cosmological parameters from complex simulations.
method Using Bayesian Neural Networks on The Quijote simulations.
result Demonstrates BNNs' ability to estimate associated uncertainties and complex output distributions.
Study of 2+1 dimensional cosmologies with positive cosmological constant, proving asymptotic convergence to de Sitter.
problem Asymptotic behavior of 2+1 dimensional cosmologies with positive cosmological constant.
method Mean Curvature Flow methods.
result Spatial slices asymptotically converge to de Sitter, becoming physically indistinguishable from it.
Paper introduces a new cosmological volume function and its properties.
problem Introducing a new cosmological volume function.
method Introduces and analyzes the cosmological volume function τ_V, showing it's continuously differentiable.
result τ_V leads to a canonical splitting of the metric tensor and a canonical Wick-rotated Riemannian metric.
Study of Einstein equations in warped spaces to determine cosmological constants.
problem Understanding the origin of the cosmological constant in higher dimensions.
method Classification and analysis of (m+n)D and (1+n)D warped spaces satisfying Einstein equations. result Warping function can determine both (m+n)D and 4D cosmological constants. Study finds solutions for spacetimes with negative cosmological constant.
problem Existence of spacetimes with negative cosmological constant.
method Proved existence of solutions for Einstein-complex scalar field equations.
result Found large families of solutions with negative cosmological constant.
Machine learning improves accuracy in estimating cosmological parameters from dark matter distribution.
problem Accurately estimating cosmological parameters from the dark matter distribution.
method Application of deep 3D convolutional networks and distribution regression framework to volumetric dark-matter simulations.
result Machine learning techniques can estimate cosmological parameters with comparable or higher accuracy than maximum-likelihood methods.
The paper defines mass for certain spacetimes with positive cosmological constant.
problem Defining mass for specific spacetimes with positive cosmological constant.
method Proposes and discusses a mass definition for compact static metrics with positive cosmological constant.
result Characterizes de Sitter solution as the only static vacuum metric with zero mass.
Machine learning enhances cosmology through new tools and data analysis.
problem Leveraging machine learning in cosmology for better understanding of the universe.
method Development of new computational tools, data analysis techniques, and community building.
result Substantial potential in cosmology remains untapped with machine learning.
SU(2) flat connections link to 3D geometry with cosmological constant.
problem Mapping flat connections on Riemann surfaces to 3D twisted geometry.
method Relating flat connection quantities to geometrical quantities in discrete 3D space.
result Moduli space of SU(2) flat connections generalizes phase space of twisted geometry.
Study how past eon's matter affects present eon in Penrose's cyclic cosmology.
problem Determining present eon's matter content from past eon's matter.
method Use Penrose's reciprocity hypothesis to link past and present eons' matter.
result Perfect fluid matter content of past eon influences present eon's matter content.
New mass definition for negative cosmological constant spacetimes.
problem Defining quasilocal mass for spacetimes with negative cosmological constant.
method Spinorial approach based on previous work for vanishing cosmological constant.
result Non-negative mass, equal to Misner-Sharp mass in spherical symmetry, zero for AdS.
Study of spacetimes in cosmology without symmetry assumptions.
problem Proving timelike incompleteness and properties of time functions.
method Rigorous mathematical proofs and analysis of spacetime properties.
result Timelike incompleteness for specific spacetimes with mean curvature constraints.
Researchers found infinite families of non-singular static spacetimes with negative cosmological constant.
problem Finding non-singular static spacetimes with negative cosmological constant.
method Constructing infinite-dimensional families of solutions to the Einstein-Maxwell equations.
result Infinite-dimensional families of non-singular static space times with negative cosmological constant.
Paper shows peeling property for Bondi-Sachs metrics with nonzero cosmological constant.
problem Investigating the peeling property of Bondi-Sachs metrics with cosmological constant.
method Using Sommerfeld's radiation condition and three nontrivial functions, constructing nonstationary vacuum metrics.
result Peeling property holds for Bondi-Sachs metrics with nonzero cosmological constant.
Study shows how 3+1D cosmologies can evolve to de Sitter space under certain conditions.
problem Understanding the evolution of 3+1D cosmologies with specific symmetry constraints.
method Mean Curvature Flow methods applied to cosmologies with positive cosmological constant and specific symmetry groups.
result Asymptotically, 3+1D cosmologies evolve to de Sitter space under certain conditions.
New CMC existence result for expanding cosmological spacetimes.
problem Establishing a new constant mean curvature (CMC) existence result for cosmological spacetimes.
method Construction of barriers in the support sense and asymptotic limit of mean curvature flow.
result The existence of a CMC Cauchy surface in expanding cosmological spacetimes.
New non-singular spacetimes found with negative cosmological constant.
problem Finding non-singular spacetimes with a negative cosmological constant.
method Constructing infinite-dimensional families of solutions to complex equations.
result Infinite-dimensional families of non-singular stationary space-times with negative cosmological constant.
Improved formulation of spinfoam quantum gravity with cosmological constant, ensuring all amplitudes are finite and providing semiclassical asymptotics.
problem Ensuring the finiteness of spinfoam amplitudes and providing semiclassical asymptotics for quantum gravity.
method Using state-integral model of PSL(2, C) Chern-Simons theory and implementing simplicity constraint. result All spinfoam amplitudes are finite and provide semiclassical asymptotics with oscillatory terms related to the Regge action.
Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL(2,C) Chern-Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity.
The paper calculates a cosmological constant from a small exotic R^4.
problem Determining the cosmological constant from a small exotic R^4.
method Low dimensional differential topology and canonical constructions.
result The cosmological constant is a topological invariant.
We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positi…
Researchers prove a 30-year-old cosmological conjecture about spacetime.
problem The rigidity of the cosmological Hawking--Penrose singularity theorem.
method Combining global viscosity solutions and elliptic approaches.
result A timelike geodesically complete spacetime splits isometrically as a Lorentzian product.
Researchers generalize cosmological models using Finsler geometry.
problem Cosmological models that closely approximate pseudo-Riemannian geometry.
method Identifying Lie Algebra of symmetry generators for spatially homogeneous and isotropic Finsler geometries.
result Found the most general spatially homogeneous and isotropic Berwald spacetimes.