Incorporating Astrophysical Systematics into a Generalized Likelihood for Cosmology with Type Ia Supernovae

Traditional cosmological inference using Type Ia supernovae (SNeIa) have used stretch- and color-corrected fits of SN Ia light curves and assumed a resulting fiducial mean and symmetric intrinsic dispersion for the resulting relative luminosity. As systematics become the main contributors to the error budget, it has become imperative to expand supernova cosmology analyses to include a more general likelihood to model systematics to remove biases with losses in precision. To illustrate an example likelihood analysis, we use a simple model of two populations with a relative luminosity shift, independent intrinsic dispersions, and linear redshift evolution of the relative fraction of each population. Treating observationally viable two-population mock data using a one-population model results in an inferred dark energy equation of state parameter $w$ that is biased by roughly 2 times its statistical error for a sample of N $\gtrsim$ 2500 SNeIa. Modeling the two-population data with a two-population model removes this bias at a cost of an approximately $\sim20\%$ increase in the statistical constraint on $w$. These significant biases can be realized even if the support for two underlying SNeIa populations, in the form of model selection criteria, is inconclusive. With the current observationally-estimated difference in the two proposed populations, a sample of N $\gtrsim$ 10,000 SNeIa is necessary to yield conclusive evidence of two populations.