Testing the Geometry of the Universe with Curvature-Consistency Relations

The Lambda cold dark matter (LCDM) cosmological model faces increasingly significant and robust tensions among independent cosmological measurements, 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 spacetime geometry at the largest scales, and in particular testing the assumption that observables (distances, redshifts, etc.) on the largest scales are described by a single Friedmann-Lemaître-Robertson-Walker (FLRW) metric.

This can however be done employing curvature-consistency tests. Such tests utilize that spatial curvature within the FLRW metrics take a particularly simple form, which implies that certain constraint equations for cosmological observables must be satisfied if the FLRW ansatz is indeed correct. In non-FLRW models, these constraints are generally expected to be violated, but theoretical predictions for the signature of their violation in non-FLRW scenarios have been lacking in the literature.

I will present recent theoretical developments on curvature-consistency tests, with focus on their signatures within physically motivated non-FLRW scenarios. In particular, I will present smoking gun signatures for back reaction universe models (where the large-scale expansion of the cosmology is different from FLRW) and the so-called Dyer-Roeder universes (where the optical properties of the cosmology deviate from the expectations of FLRW). I will finally comment on recent observational constraints of curvature-consistency tests and their implications.