PUB - Publikationen an der Universität Bielefeld

In standard cosmology a background geometry is used to interpret observations of the large scale structure of the Universe. The background means a homogeneous, isotropic and flat Friedmann-Lemaître (FL) Universe, neglecting the details at small scales and local inhomogeneities of mass density. Observational cosmology is based on light trajectories and the paths of light are null geodesics. One of the significant effects of inhomogeneity is on the light trajectories. Some aspects of this are very well understood and studied in great depth. For instance, CMB photons are related to density fluctuations by the Sachs-Wolfe effect, and gravitational lensing plays an important role for light propagation in the Universe. Cosmic structures determine how light propagates through the Universe and consequently must be taken into account. In the standard cosmological model at the largest scales, such structures are either ignored or treated as small perturbations to an isotropic and homogeneous Universe. This isotropic and homogeneous model is commonly assumed to emerge from some averaging process at the largest scales. However, averaging in general relativity is not a simple operation, due to the covariance of the theory and the non-linearity of Einstein equations. We review previous studies of the averaging and backreaction problem in cosmology. We also discuss some recent attempts, which addressed the averaging problem through propagation of light. Unfortunately, those works are restricted to either a toy model or a perturbative approach. We then present our work on a more general result for the propagation of light in an averaged Universe. We assume that there exists an averaging procedure that preserves the causal structure of space-time. Based on that assumption, we study the effects of averaging the geometry of space-time and derive an averaged version of the null geodesic equation of motion. For the averaged geometry we then assume a flat FL model and find that light propagation in this averaged FL model is not given by null geodesics of that model, but rather by a modified light propagation equation that contains an effective Hubble expansion rate, which differs from the Hubble rate of the averaged space-time.