A Nearly Model-Independent Characterization of Dark Energy Properties as a Function of Redshift

Understanding the acceleration of the universe and its cause is one of the key problems in physics and cosmology today, and is best studied using a variety of mutually complementary approaches. Daly and Djorgovski (2003, 2004) proposed a model independent approach to determine the expansion and acceleration history of the universe and a number of important physical parameters of the dark energy as functions of redshift directly from the data. Here, we apply the method to explicitly determine the first and second derivatives of the coordinate distance with respect to redshift, y^′ and y^″, and combine them to solve for the kinetic and potential energy density of the dark energy as functions of redshift, K (z) and V (z). A data set of 228 supernova and 20 radio galaxy measurements with redshifts from zero to 1.79 is used for this study. Values of y^′ and y^″ are combined to study the dimensionless acceleration rate of the universe as a function of redshift, q (z). The only assumptions underlying our determination of q (z) are that the universe is described by a Robertson-Walker (RW) metric and is spatially flat. We find that the universe is accelerating today, and was decelerating in the recent past. The transition from acceleration to deceleration occurs at a redshift of about z_T = 0.42 ±_0.06^0.08. Values of y^′ and y^″ are combined to determine K (z) and V (z). These are shown to be consistent with the values expected in a standard Lambda Cold Dark Matter (LCDM) model.