Observations in statistically homogeneous, locally inhomogeneous cosmological toy models without FLRW backgrounds

We study observations in toy models that constitute exact cosmological solutions to the Einstein equation. These models are statistically homogeneous but locally inhomogeneous, without an a priori introduced Friedmann-Lemaître-Roberston-Walker (FLRW) background and with 'structures' evolving fairly slowly. The mean redshift-distance relation and redshift drift along 500 light rays in each of two models are compared with relations based on spatial averages. The relations based on spatial averages give a good reproduction of the mean redshift-distance relation, although most convincingly in the model where the kinematical backreaction and average spatial curvature cancel each other to a subpercentage precision. In both models, the mean redshift drift clearly differs from the drift of the mean redshift. This indicates that redshift drift could be an important tool for testing the backreaction conjecture as redshift drift appears to distinguish between local and global effects. The method presented for computing the redshift drift is straightforward to generalize and can thus be utilized to fairly easily compute this quantity in a general space-time.