Do Type-Ia Supernovae Constrain the Total Equation of State?

In this paper, we consider a couple of alternative dark energy models using the total equation of state of the cosmological fluid, $\wt$. These models are fit to the recent type-Ia supernovae data and are compared to previously considered models. The first model is based on the hyperbolic tangent and provides a good estimate of the rate of the transition to dark energy domination. The second model is a cubic spline model. This model demonstrates and quantifies the non-monotonicity in the total equation of state coming from the supernovae observations. At present, the supernovae observations indicate significance to non-monotonically decreasing dark energy. We derive constraints on the spline paramters and compare and constrast the results to the Cosmological Constant dark energy model. Both the hyperbolic and splines models indicate that a precise physical notion of dark enegy is a potentially ever more mysterious quantity?