No evidence for missing covariance in the Pantheon+ SuperNova sample distance moduli

Inspired by the discussion in the community on possible hidden systematic errors in late universe cosmological probes and non-trivial physical models developed to reduce the Hubble tension, we investigate the Pantheon and Pantheon+ SNe samples for possible deviations from the original \(\Lambda\)CDM analysis. To simultaneously account for possible systematics or deviations from \(\Lambda\)CDM, we adopt Gaussian processes to model additional covariance while making no further assumptions on their origin. We explore both stationary and non-stationarity corrections to the covariance. While small changes in the inferred cosmological parameters \(H_0\) and \(\Omega_{m}\) can occur, we find no statistically significant evidence for missing covariance. We find an upper limit for the Gaussian processes amplitude \(\sigma < 0.031\) mag with \(95\%\) confidence, which corresponds to \(20\%\) of the average statistical error in the Pantheon+ sample. The strongest effect we find on the inferred cosmological parameter posterior can reduce the statistical significance of the Hubble tension between Pantheon+ and Planck estimates from 5.3\(\sigma\) to 4.5\(\sigma\). Therefore, we conclude that the SN cosmological parameter inference is robust against the analysis modifications studied in this work.