Baryon acoustic oscillation methods for generic curvature: Application to the SDSS-III Baryon Oscillation Spectroscopic Survey

We develop methods for investigating baryon acoustic oscillation (BAO) features in cosmological models with non-trivial curvature: models that are not necessarily flat, close to flat, nor with constant spatial curvature. The class of models to which our methods apply include Lemaître-Tolman-Bondi models, modified gravity cosmologies, and inhomogeneous cosmologies with backreaction - in which we do not have a prediction of the shape of the spatial 2-point correlation function, but where we nevertheless expect to see a BAO feature in the present-day galaxy distribution, in form of an excess in the galaxy 2-point correlation function. We apply our methods to the Baryon Oscillation Spectroscopic Survey (BOSS) dataset, investigating both the Lambda Cold Dark Matter (ΛCDM) and timescape cosmological models as case studies. The correlation functions measured in the two fiducial models contain a similarly-pronounced BAO feature. We use the relative tangential and radial BAO scales to measure the anisotropic Alcock-Paczyński distortion parameter, ε, which is independent of the underlying BAO preferred scale. We find that ε is consistent with zero in both fiducial cosmologies, indicating that models with a different spatial curvature behaviour can account for the relative positions of the tangential and radial BAO scale. We validate our methods using ΛCDM mocks