Exploring Cosmological Tensions with Hubble Parameter Tomography via Linear Cosmography

Given the persistence of various tensions in the "Cosmic Concordance" -- such as the "Hubble Tension", and possible departures from LambdaCDM time evolution -- seen from combinations of complementary data sets (e.g., Cosmic Microwave Background, Baryon Acoustic Oscillations, Type Ia Supernovae), it remains an ongoing possibility for these to have a real cosmological origin. If one assumes such deviations to be real, a model-independent formalism (cosmography) is useful for locating the source of the problem with concordance cosmology. The extraordinarily good fit of LambdaCDM to CMB data shows that it was a successful model of the universe at high redshift. Yet at lower redshift -- when the dark energy density becomes significant, and its precise physical nature becomes important -- the universe may have gone off the track of simple LambdaCDM. Here we use linear cosmography fits to binned Supernova data to reconstruct the detailed temporal history of the Hubble parameter, probing for interesting time-dependent behaviors of the expansion rate during and after the onset of cosmic acceleration. Using combined Type Ia supernovae from the Dark Energy Survey 5-Year data release and the Union2.1 compilation, we find intriguing hints of oscillations in the Hubble parameter during the acceleration era. While these hints are of limited statistical significance, and not robust under different redshift binnings, we present this work as a proof-of-concept demonstration of this method for reconstructing the Hubble parameter evolution, which may be useful for the voluminous Supernova data sets anticipated to become available during the next few years.