Testing inhomogeneous cosmography in our cosmic neighborhood using CosmicFlows-4

TL;DR

This work tests the convergence of the third-order general cosmographic expansion of the luminosity distance in a realistic, inhomogeneous local Universe constructed from CosmicFlows-4. By mapping density and velocity fields onto a weak-field perturbed FLRW spacetime and ray-tracing along multiple light rays, the study shows that convergence breaks down at surprisingly low redshifts along many directions, though strong smoothing (coarser grids) can extend accuracy to ~$z\sim0.1$ in some cases. The results reveal large sky-variance in the observer-based cosmographic parameters $\mathcal{H_O}$ and $\mathcal{Q_O}$ and highlight that polynomial fits to data may not faithfully recover true cosmographic coefficients unless convergence is ensured. Overall, the paper underscores that convergence must be explicitly tested in realistic analyses and that relying solely on FLRW cosmography risks losing substantial information about the cosmic environment; it also suggests that fitted coefficients reflect an implicit smoothing scale rather than universal cosmographic values. The findings have practical implications for low-redshift cosmography and for interpreting cosmographic coefficients in real data, depending on the dataset and smoothing scale used.

Abstract

The convergence of the third order general cosmographic expansion of the luminosity distance is examined using several versions of a semi-realistic model of our local cosmic neighborhood, based on publicly available density and velocity fields from CosmicFlows-4. The study supports earlier findings that the general cosmographic expansion diverges at surprisingly low redshifts, often well before z = 0.1. By being based on a realistically placed observer within a data-informed cosmic environment, the results underscore that convergence must be a central concern when applying the general cosmographic expansion. By showing all-sky maps of kinematic parameters, the study also highlights the substantial information we lose when relying solely on standard FLRW-based cosmography. Poor convergence does not necessarily render the information extracted by fitting data to the general cosmographic expansion meaningless. Rather, it calls for caution in interpreting this information, particularly regarding the physical meaning of the fitting coefficients, the physical scales they probe and the implicit smoothing introduced by the fit.

Figures (14)

• Figure 1: Two-dimensional slice of model universe corresponding to the middle plot in figure 2 of fields. A star indicates our position at supergalactic coordinates (SGX, SGY, SGZ) = (0,0,0). The plot to the left shows the slice for ungrouped data while the plot to the right shows the fields for the grouped data.
• Figure 2: Density contrast and relative deviations between exact redshift-distance relation and cosmographic expansions (denoted as "cosmo") along two fiducial lines of sight in model based on linear interpolation and N = 64.
• Figure 3: Relative deviation between the exact luminosity distance ($D_L$) and the cosmographic expansion ("cosmo") at first, second and third order along ray 1 using an N = 8 and N = 16, and different interpolation schemes. The results are shown both using grouped ("grouped") and ungrouped (not indicated) data.
• Figure 4: Relative deviation between the exact luminosity distance ($D_L$) and the cosmographic expansion ("cosmo") at first, second and third order along ray 2 using grids with N = 8 and N = 16 and different interpolation schemes. Results are shown both using grouped ("grouped") and ungrouped (not indicated) data.
• Figure 5: Relative deviation between the exact luminosity distance ($D_L$) and the cosmographic expansion ("cosmo") at first, second and third order using cubic interpolation on the N = 4 grid. Hatched areas show the fluctuation along all light rays while the shaded area shows a standard deviation around the mean which is also plotted.