Numerically reconstructing the ΛLTB metric from observations

Tue, 09/06/2015 - 12:00
Landman Bester

Abstract: The problem of reconstructing the background cosmological metric directly from observations is known as the inverse problem in cosmology. This talk will be on the inverse problem in spherically symmetric dust universes that may include a cosmological constant. Such models of the universe, otherwise known as ΛLTB models, can be used to test the validity of the Copernican principle. I will begin by introducing the ΛLTB model in observational coordinates and specify the data required to find its general relativistic solution. The focus of the talk will then shift to how Gaussian process priors can be used to smooth the data in a way that doesn’t violate any physical constraints. These smoothed functions can then be used to set the initial conditions of a numerical integration scheme that solves the Einstein field equations in observational coordinates. To finish I present an algorithm that utilises a Monte-Carlo experiment to find the full distributions of metric components inside the past lightcone.