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.
Study shows current simulations are insufficient for optimal neural network training in cosmology.
problem Insufficient training data for neural networks in cosmological inference.
method Empirical neural scaling law and Cramer-Rao bound to forecast training simulations needed.
result Current simulation suites do not provide sufficient training data for optimal neural network performance.
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.
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.
New vacuum spacetimes without CMC Cauchy surfaces found.
problem Finding vacuum cosmological spacetimes without CMC Cauchy surfaces.
method Extended construction of [6] using spatial topologies M#M. result Obtained a large class of vacuum cosmological spacetimes.
Genetic algorithms optimize neural networks for cosmological data analysis.
problem Inaccurate results from neural networks due to poor hyperparameter selection.
method Used genetic algorithms to optimize hyperparameters of neural networks.
result Genetic algorithms improve neural network performance in cosmological data analysis.
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.
New mass-type invariants for cosmological space-times.
problem Characterize de Sitter solutions in space-times with a cosmological constant.
method Introduce new mass-type invariants and prove positive mass theorems.
result 1-harmonic Mass provides new characterizations and inequalities.
We study the Laplace spectra of the intrinsic instantaneous metrics on the event and cosmological horizons of a Kerr-Newman de Sitter space-time and prove that the spectral data from these horizons uniquely determine the space-time. This is accomplished by exhibiting formulae relating the parameters of the space-time m…
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 Bondi-Sachs formalism for massless scalar field with zero cosmological constant.
problem Analyzing the Bondi-Sachs formalism for Einstein's massless scalar field equations.
method Asymptotic expansions and peeling property for Bondi-Sachs metrics and scalar fields.
result Positivity of Bondi energy-momentum under specific conditions.
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.
TRIM improves interpretability of deep neural networks in cosmology.
problem Understanding which features a deep neural network uses in a transformed space.
method TRIM (Transformation IMportance) attributes importances to features in a transformed space.
result Combining TRIM with contextual decomposition helps identify physical features learned by DNNs.
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.
Deep learning and genetic algorithms speed up cosmological Bayesian inference.
problem Substantial computational demands in Bayesian inference for cosmological parameter estimation.
method Deep learning using feedforward neural networks to approximate likelihood functions dynamically, optimized with genetic algorithms.
result Significant speed-up in Bayesian inference process for cosmological models and datasets.
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.
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in thr…
New energy definition for expanding de Sitter spacetime with umbilic boundaries.
problem Defining energy for spacetimes with expanding de Sitter background and umbilic boundaries.
method Adapting Liu-Yau energy to a quasi-local setting in expanding de Sitter spacetime.
result Positivity of the defined energy for certain values of the cosmological constant.
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.
New method extracts cosmological information from dark matter halo catalogues using graph neural networks.
problem Quantifying cosmological information from large-scale structure data.
method Implicit likelihood approach with Information Maximising Neural Networks (IMNNs) on graph representations of dark matter halo catalogues.
result Graph neural network summaries can extract information from noisy catalogues and improve parameter constraints.
We study Einstein's equation in (m+n)D and (1+n)D warped spaces (Mˉ,gˉ) and classify all such spaces satisfying Einstein equations Gˉ=−Λˉgˉ. We show that the warping function not only can determine the cosmological constant Λˉ but also it can determine the cosmological constant Λ a…
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.
Classifies cosmological Finsler spacetimes, finding viable non-stationary models.
problem Locating viable non-stationary Finsler spacetimes in cosmology.
method Locally classified all possible cosmological homogeneous and isotropic Landsberg-type Finsler structures in 4-dimensions.
result Identified unique Finsler, non-Berwaldian Landsberg generalization of Friedmann-Lemaitre-Robertson-Walker geometry.
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.
Simplified proof of cosmic singularity theorem using new mathematical techniques.
problem Proving cosmic singularity in expanding spacetimes with positive cosmological constant.
method Unified approach using the positive resolution of the virtual positive first Betti number conjecture.
result The theorem holds without the need for a spherical Cauchy surface.
Method trains emulators to estimate posterior probabilities safely.
problem Uncertainty in slow forward model calculations.
method Trains emulators while estimating posterior probabilities with MCMC, propagating error.
result Demonstrates robust posterior inference for ΛCDM cosmology model. The paper introduces a new method to characterize cosmological models using observer-based invariants.
problem Equivalence problem for cosmological models in four-dimensional gravity theories.
method Modified Cartan-Karlhede algorithm adapted to fundamental observers, including derivatives of the time-like vector field.
result A list of invariants that completely characterize cosmological models, independent of coordinates.
In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as the only static vacuum metric with zero mass. Finally, we show how to adapt our analysis to the case of negative cosmological constant, leadin…
The study examines conditions that prevent null geodesic lines in spacetimes, impacting cosmological geometry.
problem Preventing the existence of null geodesic lines in spacetimes.
method Identifying geometric conditions on foliations of spacetimes that prevent null geodesic lines, especially for spacetimes with compact Cauchy hypersurfaces.
result Conditions on foliations can prevent null geodesic lines, leading to restrictions on cosmological spacetime geometry.
We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data symmetric with respect to the toroidal directions. We obtain effective Einsteinia…
Study compares MCMC and nested sampling for high-dimensional physics problems.
problem Efficiently sampling high-dimensional Bayesian posterior distributions in particle physics and cosmology.
method Review and comparison of MCMC and nested sampling techniques on high-dimensional test functions and real physics examples.
result Modern MCMC algorithms can outperform nested sampling in certain cases, highlighting implementation details.
Study cosmic structures using Topological Data Analysis and Persistence Energy.
problem Investigate cosmic web evolution in ΛCDM cosmologies. method Apply LITE method to embed persistence diagrams into vector spaces and analyze cosmic structures.
result Discover a correlation between Persistence Energy and redshift values.
This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as…
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Ri…
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.
New findings on static near horizon geometries and quasi-Einstein manifolds, including rigidity results for negative cosmological constant.
problem Rigidity of quasi-Einstein manifolds under different cosmological constant conditions.
method Analysis of quasi-Einstein equations on closed manifolds, focusing on static vacuum solutions and their properties.
result For negative cosmological constant, rigidity holds under specific conditions on the 1-form \(X\), including incompressibility, constant norm, and nontrivial cohomology.
We show that there are isometrically nonequivalent Robertson-Walker metrics which have the same set of geodesics. While one of these metrics satisfies the Einstein equations of pure dust without a cosmological constant, all the other describe pure dust with additional energy momentum tensor of cosmological constant typ…
New formulation of Schrödinger connections preserves vector lengths in geometry.
problem Preserving vector lengths in non-Euclidean geometries.
method Coordinate-free formulation, differential geometry, torsion, non-metricity.
result Explicit example of non-static Einstein manifold with torsion.
The polynomial affine model of gravity is explored in 3D, focusing on cosmological solutions.
problem Exploring deviations from general relativity in a 3D context.
method Developed a polynomial affine model of gravity, applied to homogeneous isotropic cosmological models, and classified solutions.
result Explicit solutions derived from the connection allow the definition of alternative/emergent metrics.
A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for the metric coefficients in Fermi coordinates are derived. Sharp uni…
In this global study of solutions to the linear wave equation on Schwarzschild de Sitter spacetimes we attend to the cosmological region of spacetime which is bounded in the past by cosmological horizons and to the future by a spacelike hypersurface at infinity. We prove an energy estimate capturing the expansion of th…
Linearized Einstein equations simplified via Calabi operator.
problem Linearizing Einstein equations for cosmological applications.
method Using the Calabi operator from projective differential geometry.
result Linearized Einstein equations simplified.
In this paper, we show that the peeling property still holds for Bondi-Sachs metrics with nonzero cosmological constant under the boundary condition given by Sommerfeld's radiation condition together with three nontrivial Λ-independent functions B, a, b. This should indicate the new boundary condition is natura…
We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.