Supernova Ia constraints on a time-variable cosmological "constant"

The energy density of a scalar field phi with potential V(phi) proportional to phi(-alpha), alpha > 0, behaves like a time-variable cosmological constant that could contribute significantly to the present energy density. Predictions of this spatially flat model are compared to recent Type Ia supernova apparent magnitude versus redshift data. A large region of model parameter space is consistent with current observations. (These constraints are based on the exact scalar held model equations of motion, not on the widely used time-independent equation of state fluid approximation equations of motion.) We examine the consequences of also incorporating constraints from recent measurements of the Hubble parameter and the age of the universe in the constant and time-variable cosmological constant models. We also study the effect of using a noninformative prior for the density parameter.