Constraints on the Physical Parameters of the Dark Energy Using a   Model-Independent Approach
  Understanding the physical nature of the dark energy which appears to drive the accelerated expansion of the unvierse is one of the key problems in physics and cosmology today. This important problem is best studied using a variety of mutually complementary approaches. Daly and Djorgovski (2003, 2004) proposed a model independent approach to determine a number of important physical parameters of the dark energy as functions of redshift directly from the data. Here, we expand this method to include the determinations of its potential and kinetic energy as functions of redshift. We show that the dark energy potential and kinetic energy may be written as combinations of the first and second derivatives of the coordinate distance with respect to redshift. We expand the data set to include new supernova measurements, and now use a total of 248 coordinate distances that span the redshift range from zero to 1.79. First and second derivatives of the coordinate distance are obtained as functions of redshift, and these are combined to determine the potential and kinetic energy of the dark energy as functions of redshift. An update on the redshift behavior of the dimensionless expansion rate E(z), the acceleration rate q(z), and the dark energy pressure p(z), energy density f(z), and equation of state w(z) is also presented. We find that the standard Omega = 0.3 and Lambda = 0.7 model is in an excellent agreement with the data. We also show tentative evidence that the Cardassian and Chaplygin gas models in a spatially flat universe do not fit the data as well. 
Ruth A. Daly and S. G. Djorgovski