Related papers: Numerical Strategies of Computing the Luminosity D…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
The luminosity distance vs. redshift law is now measured using supernovae and gamma ray bursts, and the angular size distance is measured at the surface of last scattering by the CMB and at z = 0.35 by baryon acoustic oscillations. In this…
We describe a numerical algorithm which simulates the propagation of light in inhomogeneous universes, using the multiple lens-plane method. The deformation and deflection of light beams as they interact with each lens plane are computed…
This paper presents numerical solutions of particular Lemaitre-Tolman models approximating a fractal behaviour along the past light cone, as discussed in paper I (0807.0866) of this series. The initial conditions of the numerical problem…
An alternative to the postulate of dark energy required to explain the accelerated expansion of the universe is to adopt an inhomogeneous cosmological model to explain the supernovae data without dark energy. We adopt a void cosmology…
We investigate the properties of cosmological distances in locally inhomogeneous universes with pressureless matter and dark energy (quintessence), with constant equation of state. We give exact solutions for angular diameter distances in…
It is shown how certain observations interpreted in the background of the Friedmann model with $\Lambda < 0 = k$ (the $\Lambda$CDM model) can be re-interpreted using the $\Lambda = 0$ Lema\^{\i}tre - Tolman (L-T) model so as to do away with…
We find initial data for numerical relativity simulations of inhomogeneous cosmologies. This involves treating an exceptional case of the general relativity constraint equations. We devise analytic and numerical methods to treat this…
The discretization of surface intrinsic PDEs has challenges that one might not face in the flat space. The closest point method (CPM) is an embedding method that represents surfaces using a function that maps points in the flat space to…
We search for a direction in the sky that exhibits parity symmetry under reflections through a plane. We use the natural estimator, which compares the power in even and odd $\ell+m$ multipoles, and apply minimal blind masking of outliers to…
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…
We give distance--redshift relations in terms of elliptic integrals for three different mass distributions of the Friedmann-Lema\^\i tre-Robertson-Walker (FLRW) cosmology. These models are dynamically pressure free FLRW on large scales but,…
The concordance (LambdaCDM) model reproduces the main current cosmological observations assuming the validity of general relativity at all scales and epochs, the presence of cold dark matter, and of a cosmological constant, equivalent to a…
In this article, we continue our investigation on how the electromagnetic waves propagate in the Friedman-Lemaitre-Robertson-Walker spacetime. Unlike the standard approach, which relies on null geodesics and geometric optics approximation,…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and…
We study several versions of the alternating direction method of multipliers (ADMM) for solving the convex problem of finding the distance between two ellipsoids and the nonconvex problem of finding the distance between the boundaries of…
As one of the probes of universe, strong gravitational lensing systems allow us to compare different cosmological models and constrain vital cosmological parameters. This purpose can be reached from the dynamic and geometry properties of…
The $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmological model has been highly successful in predicting cosmic structure and evolution, yet recent precision measurements have highlighted discrepancies, especially in the Hubble constant…
We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which…