A large number of cosmological parameters have been suggested for obtaining information on the nature of dark energy. In this work, we study the efficacy of these different parameters in discriminating theoretical models of dark energy, using both currently available supernova (SNe) data, and simulations of future observations. We find that the current data does not put strong constraints on the nature of dark energy, irrespective of the cosmological parameter used. For future data, we find that the although deceleration parameter can accurately reconstruct some dark energy models, it is unable to discriminate between different models of dark energy, therefore limiting its usefulness. Physical parameters such as the equation of state of dark energy, or the dark energy density do a good job of both reconstruction and discrimination if the matter density is known to high accuracy. However, uncertainty in matter density reduces the efficacy of these parameters. A recently proposed parameter, Om(z), constructed from the first derivative of the SNe data, works very well in discriminating different theoretical models of dark energy, and has the added advantage of not being dependent on the value of matter density. Thus we find that a cosmological parameter constructed from the first derivative of the data, for which the theoretical models of dark energy are sufficiently distant from each other, and which is independent of the matter density, performs the best in reconstructing dark energy from SNe data.
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