Exploring Cosmological Tensions with Hubble Parameter Tomography via Linear Cosmography

TL;DR

The paper tackles the Hubble tension and potential departures from $\Lambda\mathrm{CDM}$ by reconstructing the expansion history as a function of $y$-redshift using H($y$) tomography with piecewise-linear (linear cosmography) binning of Type Ia Supernovae. It introduces the $y$-redshift variable and a bin-wise fitting framework to extract $H(y)$ from SN distance moduli and supplements this with DESI DR2 BAO data to illuminate the transition epoch around $y_{Tr}\approx0.4$. The results reveal hints of an oscillatory component in $H(y)$ after the acceleration epoch and a notable BAO-driven step near the transition, though these findings depend on binning choices and data gaps. Overall, the method provides a model-independent tool to diagnose the origin of the Hubble tension and can leverage forthcoming large SN datasets to yield more definitive insights.

Abstract

Given the persistence of various tensions in the "Cosmic Concordance" -- such as the "Hubble Tension", and the possible departure from LambdaCDM time evolution -- seen when combining complementary data sets (CMB studies, Baryon Acoustic Oscillations, Type Ia Supernovae, etc.), 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 the 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, thus 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 an oscillatory pattern in the Hubble parameter during the acceleration era. While these hints are low-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.

Figures (11)

• Figure 1: Population of each bin (for trial binning with $\{ y_{init}, \Delta y \} = \{ 0.014, 0.015 \}$), versus SNIa data set, demonstrating how this combination (with duplicated SNIa removed from Union2.1) helps fill in gaps in DES5Yr redshift-space data coverage.
• Figure 2: Distance Modulus $\mu$ versus $y$-redshift for our total data set produced by combining all data from the DES5Yr and Union2.1 SNIa compilations, except for the duplicated SNIa having been removed from the Union2.1 data set. (All points shown without error bars, for clarity.)
• Figure 3: The (statistical + systematics) error covariance matrix for Bin #17 of the $\{ y_{init}, \Delta y \} = \{ 0.014, 0.015 \}$ case, covering the $y$-redshift range $y \in [0.254,0.269]$. The matrix is block diagonal -- covariances between the (entirely distinct) SNIa of the two different compilations are set to zero -- where the lower-left block represents Union2.1 SNIa, while the upper-right block represents DES5Yr data. (The numbers along the axes represent the arbitrary # of each supernova in the bin.)
• Figure 4: Linear Cosmography best-fits shown for four representative bins of interest for the $\{ y_{init}, \Delta y \} = \{ 0.014, 0.015 \}$ case: Bin #1 ($y \in [0.014,0.029]$), Bin #7 ($y \in [0.104,0.119]$), Bin #17 ($y \in [0.254,0.269]$), and Bin #26 ($y \in [0.389,0.404]$). Each plot depicts a section of our combined {DES5Yr + Union2.1} SNIa data set, plotting the Fitting Function (Eq. \ref{['EqnFitFnDefn']}) versus $y$-redshift.
• Figure 5: Summary plots containing SNIa data and linear cosmography fits for all redshift bins. Plot (a) here depicts these with $F_{fit}$ as the vertical axis, while Plot (b) shows this axis transformed back into distance modulus $\mu$. Plots (c) and (d) show each of these, respectively, with the SNIa data removed for visual clarity.