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Traditional cosmological inference using Type Ia supernovae (SNeIa) have usedstretch- and color-corrected fits of SN Ia light curves and assumed a resultingfiducial mean and symmetric intrinsic dispersion for the resulting relativeluminosity. As systematics become the main contributors to the error budget, ithas become imperative to expand supernova cosmology analyses to include a moregeneral likelihood to model systematics to remove biases with losses inprecision. To illustrate an example likelihood analysis, we use a simple modelof two populations with a relative luminosity shift, independent intrinsicdispersions, and linear redshift evolution of the relative fraction of eachpopulation. Treating observationally viable two-population mock data using aone-population model results in an inferred dark energy equation of stateparameter $w$ that is biased by roughly 2 times its statistical error for asample of N $ \gtrsim$ 2500 SNeIa. Modeling the two-population data with atwo-population model removes this bias at a cost of an approximately $\sim20\%$increase in the statistical constraint on $w$. These significant biases can berealized even if the support for two underlying SNeIa populations, in the formof model selection criteria, is inconclusive. With the currentobservationally-estimated difference in the two proposed populations, a sampleof N $ \gtrsim$ 10,000 SNeIa is necessary to yield conclusive evidence of twopopulations.

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