Beyond H 0 and q 0: Cosmology is No Longer Just Two Numbers

For decades, H ₀ and q ₀ were the quest of cosmology, as they promised to characterize our "world model" without reference to a specific cosmological framework. Using Monte Carlo simulations, we show that q ₀ cannot be directly measured using distance indicators with both accuracy (without offset away from its true value) and precision (small error bar). While H ₀ can be measured with accuracy and precision, to avoid a small bias in its direct measurement (of order 5%) we demonstrate that the pair H ₀ and Ω _M (assuming flatness and w = -1) is a better choice of two parameters, even if our world model is not precisely ΛCDM. We illustrate this with analysis of the Constitution set of supernovae and indirectly infer q ₀ = -0.57 ± -0.04. Finally, we show that it may be possible to directly determine q ₀ with both accuracy and precision using the time dependence of redshifts ("redshift drift").