BiGONLight: light propagation with bi-local operators in Numerical Relativity

BiGONLight, Bilocal Geodesic Operators framework for Numerical Light propagation, is a new tool for light propagation in Numerical Relativity. The package implements the Bi-local Geodesic Operators formalism, a new framework for light propagation in General Relativity. With BiGONLight it is possible to extract observables such as angular diameter distance, luminosity distance, magnification as well as new real-time observables like parallax and redshift drift within the same computation. As a test-bed for our code we consider two exact cosmological models, the ΛCDM and the inhomogeneous Szekeres model, and a simulated dust universe. All our tests show an excellent agreement with known results.

Investigating cosmology with equation of state

The aim of this paper is to investigate the field equations of modified [Formula: see text] theory of gravity, where R and [Formula: see text] represent the Ricci scalar and scalar potential, respectively. We consider the Friedmann–Robertson–Walker space–time for finding some exact solutions by using different values of equation of state parameter. In this regard, different possibilities of the exact solutions have been discussed for dust universe, radiation universe, ultra-relativistic universe, sub-relativistic universe, stiff universe, and dark energy universe. Mainly power law and exponential forms of the scale factor are chosen for the analysis.

SOLVING THE INVERSE PROBLEM WITH INHOMOGENEOUS UNIVERSES

We construct the Lemaître-Tolman-Bondi (LTB) dust universe whose distance-redshift relation is equivalent to that in the concordance Λ cold dark matter (ΛCDM) cosmological model. In our model, the density distribution and velocity field are not homogeneous, whereas the big-bang time is uniform, which implies that the universe is homogeneous at its beginning. We also study the temporal variation of the cosmological redshift and show that, by the observation of this quantity, we can distinguish our LTB universe model from the concordance ΛCDM model, even if their redshift-distance relations are equivalent to each other.

A REVIEW ON THE GEOMETRIC FORMULATION OF TOLMAN–BONDI EQUATIONS IN GENERAL RELATIVITY

This work is focused on spherically symmetric space-times. More precisely, geometric and structural properties of spatially spherical shells of a dust universe are analyzed in detail considering recent results of our research. Moreover, exact solutions, obtained for constant Ricci principal curvatures, are inferred and qualitatively analyzed through suitable classic analogies.

THE EFFECT OF STRUCTURE FORMATION ON THE EXPANSION OF THE UNIVERSE

Observations of the expansion rate of the universe at late times disagree by a factor of 1.5–2 with the prediction of homogeneous and isotropic models based on ordinary matter and gravity. We discuss how the departure from linearly perturbed homogeneity and isotropy due to structure formation could explain this discrepancy. We evaluate the expansion rate in a dust universe which contains nonlinear structures with a statistically homogeneous and isotropic distribution. The expansion rate is found to increase relative to the exactly homogeneous and isotropic case by a factor of 1.1–1.3 at some tens of billions of years. The time scale follows from the cold dark matter transfer function and the amplitude of primordial perturbations without additional free parameters.

COSMOLOGICAL ACCELERATION FROM STRUCTURE FORMATION

We discuss the Buchert equations, which describe the average expansion of an inhomogeneous dust universe. In the limit of small perturbations, they reduce to the Friedmann–Robertson–Walker equations. However, when the universe is very inhomogeneous, the behavior can be qualitatively different from the FRW case. In particular, the average expansion rate can accelerate even though the local expansion rate decelerates everywhere. We clarify the physical meaning of this paradoxical feature with a simple toy model, and demonstrate how acceleration is intimately connected with gravitational collapse. This provides a link to structure formation, which in turn has a preferred time around the era when acceleration has been observed to start.