We introduce a generalization of the 4−dimensional averaging window function of Gasperini, Marozzi and Veneziano (2010) that may prove useful for a number of applications. The covariant nature of spatial scalar averaging schemes to address the averaging problem in relativistic cosmology is an important property that is implied by construction, but usually remains implicit. We employ here the approach of Gasperini et al. for two reasons. First, the formalism and its generalization presented here are manifestly covariant. Second, the formalism is convenient for disentangling the dependencies on foliation, volume measure, and boundaries in the averaged expressions entering in scalar averaging schemes. These properties will prove handy for simplifying expressions, but also for investigating extremal foliations and for comparing averaged properties of different foliations directly. The proposed generalization of the window function allows for choosing the most appropriate averaging scheme for the physical problem at hand, and for distinguishing between the role of the foliation itself and the role of the volume measure in averaged dynamic equations. We also show that one particular window function obtained from this generalized class results in an averaging scheme corresponding to that of a recent investigation by Buchert, Mourier and Roy (2018) and, as a byproduct, we explicitly show that the general equations for backreaction derived therein are covariant.

Parameters that quantify the acceleration of cosmic expansion are conventionally determined within the standard Friedmann-Lemaıtre-Robertson-Walker (FLRW) model, which fixes spatial curvature to be homogeneous. Generic averages of Einstein’s equations in inhomogeneous cosmology lead to models with non-rigidly evolving average spatial curvature, and different parametrizations of apparent cosmic acceleration. The timescape cosmology is a viable example of such a model without dark energy. Using the largest available supernova data set, the Joint Light-curve Analysis (JLA) catalogue, we find that the timescape model fits the luminosity distance-redshift data with a likelihood that is statistically indistinguishable from the standard spatially flat Lambda Cold Dark Matter (ΛCDM) cosmology by Bayesian comparison. In the timescape case cosmic acceleration is non-zero but has a marginal amplitude, with best-fitting apparent deceleration parameter, q0 = −0.043 +0:004 -0:000 Systematic issues regarding standardization of supernova light curves are analysed. Cuts of data at the statistical homogeneity scale affect light curve parameter fits independent of cosmology.

A cosmological model dependence of empirical changes to the mean colour parameter is also found. Irrespective of which model ultimately fits better, we argue that as a competitive model with a non-FLRW expansion history, the timescape model may prove a useful diagnostic tool for disentangling selection effects and astrophysical systematics from the underlying expansion history.

We also perform a further analysis using the JLA catalogue. We examine the fit of a class of exact scaling solutions with dynamical spatial curvature formulated in the framework of a scalar averaging scheme for relativistic inhomogeneous space-times. In these models, global volume acceleration may emerge as a result of the non-local variance between expansion rates of clusters and voids, the latter gaining volume dominance in the late-epoch Universe. We find best-fit parameters for a scaling model of backreaction that are reasonably consistent with previously found constraints from SNIa, CMB, and baryon acoustic oscillations data. The quality of fit of the scaling solutions is indistinguishable from that of the ΛCDM model and the timescape cosmology from an Akaike Information Criterion (AIC) perspective. This indicates that a broad class of models can account for the z &#U+2272; 1 expansion history.

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 Lemaˆıtre-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 the 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 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-Paczyn´ski distortion parameter, ∈, which is independent of the underlying BAO preferred scale. We find that ∈ is consistent with zero in both fiducial cosmologies, indicating that models with a different spatial curvature evolution can account for the relative positions of the tangential and radial BAO scale. We validate our methods using ΛCDM mock catalogoues.

We investigate – in a generic setting – the regime of applicability of the Alcock-Paczyn´ski (AP) scaling conventionally applied to test different cosmological models, given a fiducial measurement of the BAO characteristic scale in the galaxy 2-point correlation function. We quantify the error in conventional AP scaling methods, for which our ignorance about the true cosmology is parameterised in terms of two constant AP scaling parameters evaluated at the effective redshift of the survey. We propose a new, and as it turns out, improved version of the constant AP scaling, also consisting of two scaling parameters. The two constant AP scaling methods are almost indistinguishable when the fiducial model used in data reduction, and the ‘true’ underlying cosmology do not differ substantially in terms of metric gradients or when the redshift range of the measurements is small. When the fiducial model and the ‘true’ model differ substantially in terms of metric gradients, the two AP scaling methods differ in general. Our new methods can be applied to existing analysis through a reinterpretation of the results of the conventional AP scaling. This reinterpretation might be important in model universes where curvature gradients above the scale of galaxies are significant (and cannot be ignored by a suitable smoothing process).

We test our theoretical findings on ΛCDM mock catalogues where the underlying space-time model is known. The conventional constant AP scaling methods are surprisingly successful for pairs of large-scale metrics, but eventually break down when pathological models which allow for large metric gradients are tested. The new constant AP scaling methods proposed in this paper are efficient for all test models examined. We find systematic errors of ∼1% in the recovery of the BAO scale when the true model is distant from the fiducial, which are not attributed to any constant AP approximation. The level of systematics is robust to the exact fitting method employed. This indicates that the error budget of the BAO acoustic scale measurements in the standard literature is underestimated.