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

Abstract

We discuss a rigorous procedure for quantifying the difference between our past light cone and the past light cone of the fiducial Friedmann–Lemaitre–Robertson–Walker spacetime, modeling the large-scale descriptions of cosmological data in the standard ΛCDM scenario. This result is made possible by exploiting the scale-dependent distance functional between past light cones 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 light cone, namely the area distance and the lensing distortion, also addressing the very delicate problem of the presence of light cone caustics. This analysis works beautifully and seems to remove several of the difficulties encountered in comparing the actual geometry of our past light cone with the geometry of the fiducial FLRW light cone 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, which may be of relevance in selecting the FLRW model that best fits the observational data.