The project addresses the problem of how current results from precision cosmology are systematically biased when ignoring nonlinear inhomogeneities in cosmic structures in the universe. We plan to develop a new framework to parameterize and remove these biases. Indeed, recent studies have shown that important cosmological parameters like the spatial curvature, the matter density parameters and the Hubble constant can be shifted by as much as 10% from their true value when these inhomogeneities are not accounted for. We will employ the well-regarded relativistic inhomogeneous cosmological models called Szekeres models since the usual Friedmann models plus small linear perturbations cannot capture these nonlinear effects. The Szekeres models have no artificial symmetry and are consistent with the cosmological principle. With my graduate student Austin Peel, we will work on both the analytical and numerical aspects of the project. The core question addressed by is how to model these biases and eliminate them. The specific activities include: (1) deriving analytical equations for observables in the Szekeres inhomogeneous cosmological models (2) developing and testing the numerical programs to solve these equations (3) Integrate the resulting products into a framework ready to use (4) apply the framework to available cosmological data sets. Concrete outputs will include a numerical code package available to the cosmology community, including a minimum set of bias parameters to control the effect of inhomogeneities. We expect at least 6 peer reviewed articles from the project plus a review. The outcomes include a new direction of research where incoming and future data can be analyzed with more accurate interpretations. For example, a measure of a non-zero spatial curvature will address the current question of flat and infinite universe. The study has the potential to lead to a significantly better understanding of the exact structure and evolution of the universe.
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