Universal distance modes from DESI BAO and Type Ia supernovae: what do cosmological rulers actually measure?

Abstract

We use an SVD decomposition of the low-redshift distance measurements from DESI BAO and three Type Ia supernova compilations to identify the leading linear directions probed by the data and to localize the tension with the LCDM CMB-anchored predictions. The leading direction V_0 -- whose data amplitude we denote c_0 -- is, to high accuracy, a measurement of Omega_m h^2: the projection of the data on V_0 probes essentially this one CMB-derived parameter combination. BAO constrains this parameter more tightly than the CMB itself; the three SN compilations do not. In every extension of LCDM we consider, the leading measurable direction remains V_0, and it is where most of the tension with the CMB resides. In the w0-wa extension a second direction V_1 becomes measurable and provides an independent test of dynamical dark energy; the data show no significant tension in this direction. The only other beyond-LCDM extension that opens a genuinely new measurable direction is spatial curvature, and only marginally and only for BAO; both measurable directions then independently prefer positive spatial curvature, though the second direction is poorly constrained.