Lossless Compression of Cosmological Information from Type Ia Supernova Distance Measurements

We perform model-independent distance measurements on four Type Ia supernovae (SNe Ia) compilations (Pantheon, Pantheon+, DES-Dovekie, Union3) and compress each dataset into the values of $\log r_p(z)$ at eleven redshift knots, where $r_p(z)$ is a rescaled comoving distance. These Gaussian distributed compressed values, together with their full covariance, completely capture the distance-redshift relation information from each dataset. We demonstrate this by using these to perform an Markov Chain Monte Carlo (MCMC) likelihood analysis to infer cosmological parameters in flat $\Lambda$CDM, flat $w_0 w_a$CDM, and a non-parametric reconstruction of the dark-energy density $X(z) \equiv \rho_{\rm DE}(z)/\rho_{\rm DE}(0)$. Across all datasets and flux-averaging configurations and all three cosmological models, the resulting parameter contours and figures of merit reproduce the corresponding full distance-modulus analyses using the original SNe Ia data sets within the statistical sampling noise of the chains, demonstrating that the eleven $\log r_p$ data points are an operationally lossless compression of the cosmological information in the dataset. Our SN Ia data compression enables an analytic analysis that completes in $O(10^{-2})$ s per dataset and reduces the downstream cosmological MCMC to the fast evaluation of an $11$-dimensional Gaussian likelihood, with a per-step cost set by the number of knots and independent of the SNe Ia sample size. Our methodology will benefit the data analysis of future surveys from Euclid, Roman, and LSST, which will deliver SNe Ia samples one to three orders of magnitude larger than current ones.