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 (but slowly varying) averaged spatial 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 Lemaitre-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 ($Λ$CDM) 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 $Λ$CDM mocks.