arXiv research

Paper introduces a new cosmological volume function and its properties.

Study of spacetimes in cosmology without symmetry assumptions.

The paper examines isotropic cosmological space-times with changing sectional curvature.

Let $(M,g)$ be a time oriented Lorentzian manifold and $d$ the Lorentzian distance on $M$. The function $τ(q):=\sup_{p< q} d(p,q)$ is the cosmological time function of $M$, where as usual $p< q$ means that $p$ is in the causal past of $q$. This function is called regular iff $τ(q) < \infty$ for all $q$ and also $τ\to 0…

We study Einstein's equation in $(m+n)D$ and $(1+n)D$ warped spaces $(\bar{M},\bar{g})$ and classify all such spaces satisfying Einstein equations $\bar{G}=-\barΛ\bar{g}$. We show that the warping function not only can determine the cosmological constant $\barΛ$ but also it can determine the cosmological constant $Λ$ a…

In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property…

This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension $n\geq 3$ with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they a…

Proves limit curve theorem for incomplete metric spaces, applies to null distance in Lorentzian manifolds.

We prove that the leaves of an inverse mean curvature flow provide a foliation of a future end of a cosmological spacetime $N$ under the necessary and sufficent assumptions that $N$ satisfies a future mean curvature barrier condition and a strong volume decay condition. Moreover, the flow parameter $t$ can be used to d…

We consider spacetimes consisting of a manifold with Lorentzian metric and a weight function or scalar field. These spacetimes admit a Bakry-Émery-Ricci tensor which is a natural generalization of the Ricci tensor. We impose an energy condition on the Bakry-Émery-Ricci tensor and obtain singularity theorems of a cosmol…

Null distance encodes causal structure in spacetimes.

New mass-type invariants for cosmological space-times.

This paper is motivated by the non-linear stability problem for the expanding region of Kerr de Sitter cosmologies in the context of Einstein's equations with positive cosmological constant. We show that under dynamically realistic assumptions the conformal Weyl curvature of the spacetime decays towards future null inf…

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four…

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…

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…

This paper continues the investigation of constant mean curvature (CMC) time functions in maximal globally hyperbolic spatially compact spacetimes of constant sectional curvature, which was started in math.DG/0604486. In that paper, the case of flat spacetimes was considered, and in the present paper, the remaining cas…

In this paper we study the flat (n+1)-spacetimes admitting a Cauchy surface diffeomorphic to a compact hyperbolic n-manifold. We show how to construct a canonical future complete one among all such spacetimes sharing the same holonomy. We study the geometry of such a spacetime in terms of its canonical cosmological tim…

The paper studies convergence of cosmological spacetimes using null distance.

New null distance bounds confirm Big Bang singularity in cosmological models.

We construct a large class of new singularity-free static Lorentzian four-dimensional solutions of the vacuum Einstein equations with a negative cosmological constant. The new families of metrics contain space-times with, or without, black hole regions. Two uniqueness results are also established.

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.

Researchers generalize cosmological models using Finsler geometry.

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…

Deep learning and genetic algorithms speed up cosmological Bayesian inference.

Unified cosmological and Einstein polytope theories.

We show that any metric on $S^2$ with Gauss curvature $K \geq -κ$ admits a $C^{1,1}$-isometric embedding into the hyperbolic space with sectional curvature $-κ$. We also give a sufficient condition for a metric on $S^2$ to be isometrically embedded into anti-de Sitter spacetime with the prescribed cosmological time fun…

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 construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

Proves globally hyperbolic spacetimes via null distance completeness.

The paper introduces a new method to characterize cosmological models using observer-based invariants.

Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.

Physics-informed neural networks improve baryonic predictions from dark matter simulations.

The universe's shape and size are determined in general cosmological models.

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…

Generalising the results in arXiv:1612.00281, we construct infinite-dimensional families of non-singular stationary space times, solutions of Yang-Mills-Higgs-Einstein-Maxwell-Chern-Simons-dilaton-scalar field equations with a negative cosmological constant. The families include an infinite-dimensional family of soluti…

Study shows current simulations are insufficient for optimal neural network training in cosmology.

Study shows inflation in 3+1D cosmologies with bounded scalar potential and specific symmetry.

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis tool in cosmology and astrophysics. Its drawback, however, is a slow convergence r…

Bayesian Neural Networks improve precision cosmology from simulations.

Genetic algorithms optimize neural networks for cosmological data analysis.

Theorem proves topological censorship for universes with positive cosmological constant.

We show that the recent work of Lee [23] implies existence of a large class of new singularity-free strictly static Lorentzian vacuum solutions of the Einstein equations with a negative cosmological constant. This holds in all space-time dimensions greater than or equal to four, and leads both to strictly static soluti…

The two-dimensional renormalization group acting as the Ricci flow $Λ\frac{\partial}{\partialΛ} g_{μν} = R_{μν}$ produces a specific 1+3 dimensional space-time metric which describes an expanding universe that starts with a big bang $a \sim t^{\scriptscriptstyle 1/\sqrt3}$ then decelerates until $z=0.2$ then accelerate…

New method extracts cosmological information from dark matter halo catalogues using graph neural networks.

Study compares MCMC and nested sampling for high-dimensional physics problems.

For a stable marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant $Λ> 0$ and with matter satisfying the dominant energy condition, we prove that the area $A$ and the angular momentum $J$ satisfy the inequality $8π|J| \le A\sqrt{(1-ΛA/4π)(1-ΛA/12π)}$ which is saturated pre…

In this paper we study non-singular vacuum static space-times with non-zero cosmological constant. We introduce new integral quantities, and under suitable assumptions we prove their monotonicity along the level set flow of the static potential. We then show how to use these properties to derive a number of sharp geome…