ΛCDM cosmological fit to Pantheon+ supernovae

What this research found

Type Ia supernovae are the standardizable candles that revealed cosmic acceleration, and the Pantheon+ compilation gathers 1,701 light curves from 18 surveys into one distance ladder together with a covariance matrix describing its correlated systematic errors. Fitting a spatially flat ΛCDM cosmology to 1,588 of those supernovae gives a present-day matter density of 0.347, with +0.019 and −0.018 uncertainty. Redoing the fit with only the diagonal errors narrows that uncertainty by about 35% and pushes the central value up by roughly 1.5 sigma, so the correlated terms change both the error bar and the answer.

• With the full statistical-plus-systematic covariance, the matter density of a flat ΛCDM model is 0.3471, spanning 0.3287 to 0.3660 at 68% confidence, with a minimum chi-squared of 1433.06 over 1,586 degrees of freedom.
• Throwing away the off-diagonal covariance terms shrinks the 68% half-width from ±0.019 to ±0.014, about 35% narrower, and raises the best fit to 0.3744 — a shift of roughly 0.027, near 1.5 sigma. Shared calibration offsets and common light-curve model errors cannot be beaten down by averaging the way independent noise can.
• Substituting the peculiar-velocity-corrected Hubble-diagram redshift for the CMB-frame redshift in the comoving-distance integral lowers the best fit to 0.3324 ± 0.018, a −0.79 sigma change. That reproduces the published Pantheon+ value of about 0.334, validating the independently built pipeline end to end, and pins local flow corrections as a sub-1-sigma systematic.
• Hubble residuals about the best fit are flat and centred on zero with a root-mean-square scatter of 0.157 mag, matching the intrinsic dispersion of standardized Type Ia supernovae and showing no redshift-dependent trend across more than two decades in redshift.
• Both fits return a reduced chi-squared below unity — 0.904 with the full covariance and 0.868 with diagonal errors — indicating the released error model is mildly conservative, so the quoted uncertainties are if anything slightly generous.

How it was done

The Pantheon+ distance table and its 1701 by 1701 covariance were taken from the official release. Supernovae below CMB-frame redshift 0.01 were cut to suppress peculiar-velocity contamination, removing 113 light curves and leaving 1,588 objects spanning redshift 0.01029 to 2.2613, with the covariance sliced on the same indices so every surviving correlation was preserved. A flat ΛCDM model leaves one free background parameter, because the supernova absolute magnitude and the Hubble constant enter only through a single additive offset to the distance modulus; that offset was marginalized analytically rather than sampled, and all inverse-covariance products were obtained by Cholesky factorization. The chi-squared was minimized over matter density on the interval from 0 to 1 with a bounded optimizer alongside a 1001-point grid scan, and the 68% interval located by root-finding where chi-squared rises by one. The procedure was then rerun twice: once with the covariance replaced by its diagonal, and once with the alternative redshift definition.

Data sources

• Pantheon+/SH0ES data release, August 2022 version 1 — 1,701 light curves of about 1,550 spectroscopically confirmed Type Ia supernovae from 18 surveys, with the full statistical-plus-systematic covariance
• Brout et al., Astrophysical Journal 938:110 (2022) — published Pantheon+ cosmological constraints
• Conley et al., ApJS 192:1 (2011) — analytic marginalization of the distance-modulus offset
• Planck Collaboration 2018, Astronomy & Astrophysics 641:A6 — CMB-only matter density of 0.315 ± 0.007 used for comparison