An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix?

Abstract

We investigate the statistics of the available Pantheon+ dataset. Noticing that the ${\chi }^2$ value for the best-fit $\Lambda$CDM model to the real data is small, we quantify how significant its smallness is by calculating the distribution of ${\chi }^2$ values for the best-fit $\Lambda$CDM model fit to mock Pantheon+-like datasets, using the provided covariance matrix. We further investigate the distribution of the residuals of the Pantheon+ dataset with respect to the best-fit $\Lambda$CDM model, and notice that they scatter less than would be expected from the covariance matrix but find no significant kurtosis. These results point to the conclusion that the Pantheon+ covariance matrix is over-estimated. One simple interpretation of these results is a $\sim$7\% overestimation of errors on SN distance moduli in Pantheon+ data. When the covariance matrix is reduced by subtracting an intrinsic scatter term from the diagonal terms of the covariance matrix, the best-fit ${\chi }^2$ for the $\Lambda$CDM model achieves a normal value of 1580 and no deviation from $\Lambda$CDM is detected. We further quantify how consistent the $\Lambda$CDM model is with respect to the modified data with the subtracted covariance matrix using model-independent reconstruction techniques such as the iterative smoothing method. We find that the standard model is consistent with the data. There are a number of potential explanations for this smallness of the ${\chi }^2$, such as a Malmquist bias at high redshift, or accounting for systematic uncertainties by adding them to the covariance matrix, thus approximating systematic uncertainties as statistical ones.

11 pages, 6 figures, matches the published version. v3: fixed the wrong DOI

References in corpus (10)

• The Pantheon+ Analysis: Cosmological Constraints
• The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
• Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey
• It's Dust: Solving the Mysteries of the Intrinsic Scatter and Host-Galaxy Dependence of Standardized Type Ia Supernova Brightnesses
• The Pantheon+ Analysis: SuperCal-Fragilistic Cross Calibration, Retrained SALT2 Light Curve Model, and Calibration Systematic Uncertainty
• The Pantheon+ Analysis: Improving the Redshifts and Peculiar Velocities of Type Ia Supernovae Used in Cosmological Analyses
• Model Independent Reconstruction of the Expansion History of the Universe and the Properties of Dark Energy
• The Pantheon+ Analysis: Evaluating Peculiar Velocity Corrections in Cosmological Analyses with Nearby Type Ia Supernovae
• Binning is Sinning (Supernova Version): The Impact of Self-Calibration in Cosmological Analyses with Type Ia Supernovae
• Model-independent constraints on Type Ia supernova light-curve hyper-parameters and reconstructions of the expansion history of the Universe

Cited by in corpus (3)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Cosmology of Cubic Poincaré Gauge gravity
• Constraints on AvERA Cosmologies from Cosmic Chronometers and Type Ia Supernovae