Isolating non-linearities of light propagation in inhomogeneous cosmologies

Abstract

A new formulation for light propagation in geometric optics by means of the Bi-local Geodesic Operators is considered. We develop the BiGONLight Mathematica package, uniquely designed to apply this framework to compute optical observables in Numerical Relativity. Our package can be used for light propagation on a wide range of scales and redshifts and accepts numerical as well as analytical input for the spacetime metric. In this paper we focus on two cosmological observables, the redshift and the angular diameter distance, specializing our analysis to a wall universe modeled within the post-Newtonian approximation. With this choice and the input metric in analytical form, we are able to estimate non-linearities of light propagation by comparing and isolating the contributions coming from Newtonian and post-Newtonian approximations as opposed to linear perturbation theory. We also clarify the role of the dominant post-Newtonian contribution represented by the linear initial seed which, strictly speaking, is absent in the Newtonian treatment. We found that post-Newtonian non-linear corrections are below 1%, in agreement with previous results in the literature.

BiGONLight: light propagation with bilocal operators in numerical relativity

“…An analytical solution for the spacetime metric in any perturbative scheme can be also given as input but the code does not apply the perturbative scheme to light propagation. This is indeed the approach we adopted in reference [56]. We plan to implement perturbation theory in a future version of BiGONLight.…”

“…We are able to reach this extremely good accuracy by using the precision control options and the many well-tested numerical methods to solve ODE implemented in Mathematica. For the second test we consider the Szekeres inhomogeneous cosmological model as presented in references [56,57] and we compare the BGO formalism with the standard procedures used for the angular diameter distance and the redshift drift. Let us point out here that the BGO formalism provides a unified way to compute multiple observables within the same framework, contrary to the standard approach.…”

“…with 2 F 1 (a, b, c, y) being the Gaussian (or ordinary) hypergeometric function. The term B in equation ( 75) is constant and given by (see appendix C in [56])…”

Redshift drift in a universe with structure. II. Light rays propagated through a Newtonian N -body simulation

“…Several formalisms for computing the redshift drift in inhomogeneous cosmological models have been proposed within the previous few years [33,[51][52][53][54][55]. The redshift drift will here be computed using the formalism presented in [54], i.e.…”

Periodic boundary conditions and G 2 cosmology

“…A lot of the research to date has focused on the so-called Gowdy vacuum spacetimes [15], because such models are much more tractable than non-vacuum ones and the existence of compact space sections facilitates numerical simulations since the problem of boundary conditions at spatial infinity is avoided. Recently, a plane-parallel model (or wall Universe) [16], in which light rays pass through a series of plane-symmetric perturbations around a FLRW background, was used to study the back-reaction from the small-scale inhomogeneities [17,18].…”