Diagnostic Consistency Tests of the Concordance Cosmology

TL;DR

This paper introduces a model-independent framework to test the large-scale geometry of the universe and the FLRW assumption using derivatives of distance and expansion rate, enabling new diagnostics of cosmological models.

Contribution

It develops a novel, model-independent method combining derivatives of distance and expansion rate to test FLRW geometry without assuming dark energy or gravity theories.

Findings

Framework exposes physical content of FLRW consistency relations.

Derives a nonparametric estimator for the cosmic density field.

Provides new observational tests for departures from standard cosmology.

Abstract

The $\Lambda$CDM cosmological model faces increasingly significant and robust tensions among independent cosmological probes, prompting renewed scrutiny of its foundational assumptions. While General Relativity and the nature of dark energy are now routinely tested with cosmological surveys, less progress has been made testing the space-time geometry at the largest scales, and in particular testing the assumption that observables (distances, redshifs, expansion of space, etc.) on the largest scales are described by a single Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric. In order to enable such tests, we introduce a model-independent framework that combines successive derivatives of the angular diameter distance, $d_A(z)$, with the line-of-sight expansion rate, $\mathcal{H}(z)$, to expose the physical content of well-known FLRW consistency relations. This allows us to perform diagnostic tests of the large-scale geometry, that are free of assumptions about dark energy and the theory of gravity on large scales. In addition, we derive a new nonparametric estimator for the cosmic density field that is independent of the Friedmann equations. This enables qualitatively new, observationally accessible tests of the FLRW framework and provides a stringent, model-independent diagnostic for departures from standard cosmology using current and forthcoming distance and expansion rate measurements.