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

TL;DR

The paper investigates observations in exact, inhomogeneous cosmologies built without an explicit FLRW background to probe backreaction effects. By tessellating space into Kasner-like Bianchi I cubes and solving light propagation and redshift drift along 500 rays, it shows that spatial averages can reproduce the mean redshift-distance relation, but the redshift drift of the mean does not equal the drift of the mean redshift, signaling backreaction influence. The results imply that redshift drift can serve as a diagnostic to distinguish local inhomogeneous effects from global averaged dynamics, with the degree of agreement depending on the model’s kinematical backreaction. These findings offer a practical method to compute redshift drift in general spacetimes and emphasize the value of exact solutions for testing backreaction scenarios.

Abstract

Observations are studied in toy-models constituting exact cosmological solutions to the Einstein equation which are statistically homogeneous but locally inhomogeneous, without an a priori introduced 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 to 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 is subpercent. 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 spacetime.

Figures (3)

• Figure 1: 2D rendering of fundamental Bianchi I block with their values of $\alpha, \beta$ and $\gamma$ as well as their size and numbering ($\alpha$ takes the value a or A, $\beta$ b or B, and $\gamma$ g or G). The cubes in the left side of the figure have a comoving height of dz1, and those to the left dz2. The two sets of cubes are stacked on top of each other such that cube 1 is below cube 5 etc.
• Figure 2: Local expansion rates of each region of the fundamental blocks together with the average expansion rate of the models and the expansions of the EdS model (for comparison) and the average expansion $a_{D,t}$. For model 1, a close-up of $a_{D,t}$ is included to show that it is increasing with time.
• Figure 3: Average, mean and spread of redshift-distance relation and redshift drift along 500 light rays compared to predictions based on spatial averages. The average and mean redshift-distance relations are indistinguishable in the figure for model 1. The redshift drift was computed using $\delta t_0 = 30$yr.