A Scale-Dependent Distance Functional between Past Light Cones in Cosmology

TL;DR

This paper introduces a rigorous, scale-dependent distance functional to quantify differences between our observed past lightcone and the idealized FLRW model, addressing challenges in cosmological data comparison.

Contribution

It develops a novel harmonic map type functional expressed through observable quantities, aiding in selecting the best-fit FLRW model from cosmological data.

Findings

Functional effectively compares actual and FLRW lightcones.

Addresses lightcone caustics in the comparison.

Provides a new interpretation of the functional as a scale-dependent effective field.

Abstract

We discuss a rigorous procedure for quantifying the difference between our past lightcone and the past lightcone of the fiducial Friedmann-Lemaitre-Robertson-Walker spacetime modeling the large-scale description of cosmological data in the standard $\Lambda\mathrm{CDM}$ scenario. This result is made possible by exploiting the scale-dependent distance functional between past lightcones recently introduced by us. We express this harmonic map type functional in terms of the physical quantities that characterize the actual measurements along our past lightcone, namely the area distance and the lensing distortion, also addressing the very delicate problem of the presence of lightcone caustics. This analysis works beautifully and seems to remove several of the difficulties encountered in comparing the actual geometry of our past lightcone with the geometry of the fiducial FLRW lightcone of choice. We also discuss how, from the point of view of the FLRW geometry, this distance functional may be interpreted as a scale-dependent effective field, the pre-homogeneity field, that may be of relevance in selecting the FLRW model that best fits the observational data.