Observational constraints on the averaged universe

Abstract

Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not yield the same result as solving Einstein's equations with a smooth matter distribution, and that the smooth models we fit to observations need not be simply related to the actual geometry of spacetime. One specific consequence of this is a decoupling of the geometrical spatial curvature term in the metric from the dynamical spatial curvature in the Friedmann equation. Here we investigate the consequences of this decoupling by fitting to a combination of HST, CMB, SNIa and BAO data sets. We find that only the geometrical spatial curvature is tightly constrained, and that our ability to constrain dark energy dynamics will be severely impaired until we gain a thorough understanding of the averaging problem in cosmology.

Interpretation of the Hubble diagram in a nonhomogeneous universe

“…Similar ideas have actually been held in other contexts [84,85], and in particular regarding the spatial curvature [86,87]. We claim that the simplest Swiss-cheese models are good models to address such questions-as well as the RicciWeyl problem and the fluid approximation-with their own use, between the perturbation theory and N -body simulations.…”

Theoretical cosmology

“…As an illustration, constraints on the phenomenological two curvature model (which has a simple parametrized backreaction contribution [106] leading to decoupled spatial curvature parameters Ω kg , Ω k d in the metric and the Friedmann equation, respectively, and which reduces to the standard cosmology when Ω kg = Ω k d ), were investigated in [153]. It was found that the constraints on the two spatial curvature parameters are significantly weaker than in the standard model, with constraints on Ω kg an order of magnitude tighter than those on Ω k d , and there are tantalizing hints from Bayesian model selection statistics that the data favor Ω k d = Ω kg at a high level of confidence.…”

Data analysis and phenomenological cosmology

“…The motivation to study an phenomenological extension to the standard model is two-fold: i) There is a 3.3σ tension between the local Hubble constant from type 1a supernova and the large-scale Hubble constant obtained from the CMB [8][9][10][11]. ii) In previous works [12,13], using older Baryonic Acoustic Oscillation (BAO) data [14][15][16][17][18], it has been shown that a simple two-curvature extension to the standard model might be slightly preferred over the ΛCDM model.…”

“…In addition, [12] studied the observational viability of a simple phenomenological two-scale model with a simple parametrized backreaction contribution to the EFE with non-equal spatial curvature parameters k g and k d [13], motivated by an exact and fully covariant macroscopic averaging procedure [19]. Current constraints on spatial curvature within the standard ΛCDM model show that it is dynamically negligible: Ω k ∼ 5 × 10 −3 (95%CL) [9].…”