Some functions entering cosmological analysis , such as the dark energy equation of state or systematic uncertainties , are unknown functions of redshift .
To include them without assuming a particular form we derive an efficient method for generating realizations of all possible functions subject to certain bounds or physical conditions , e.g . w \in [ -1 , +1 ] as for quintessence .
The method is optimal in the sense that it is both pure and complete in filling the allowed space of principal components .
The technique is applied to propagation of systematic uncertainties in supernova population drift and dust corrections and calibration through to cosmology parameter estimation and bias in the magnitude-redshift Hubble diagram .
We identify specific ranges of redshift and wavelength bands where the greatest improvements in supernova systematics due to population evolution and dust correction can be achieved .