We introduce a new cosmological diagnostic pair {r, s} called Statefinder. The Statefinder is dimensionless and, like the Hubble and deceleration parameters H(z) and q(z), is constructed from the scale factor of the Universe and its derivatives only. The parameter r(z) forms the next step in the hierarchy of geometrical cosmological parameters used to study the Universe after H and q, while the parameter s(z) is a linear combination of q and r chosen in such a way that it does not depend upon the dark energy density ΩX (z). The Statefinder pair {r, s} is algebraically related to the the dark energy pressure-to-energy ratio w = p/ε and its time derivative, and sheds light on the nature of dark energy/quintessence. Its properties allow to usefully differentiate between different forms of dark energy with constant and variable w, including a cosmological constant (w = −1). The Statefinder pair can be determined to very good accuracy from a SNAP type experiment.

The coming few years are likely to witness a dramatic increase in high‐quality supernova data as current surveys add more high‐redshift supernovae to their inventory and as newer and deeper supernova experiments become operational. Given the current variety in dark energy models and the expected improvement in observational data, an accurate and versatile diagnostic of dark energy is the need of the hour. This paper examines the statefinder diagnostic in the light of the proposed SuperNova Acceleration Probe (SNAP) satellite, which is expected to observe about 2000 supernovae per year. We show that the statefinder is versatile enough to differentiate between dark energy models as varied as the cosmological constant on one hand, and quintessence, the Chaplygin gas and braneworld models, on the other. Using SNAP data, the statefinder can distinguish a cosmological constant (w=−1) from quintessence models with w≥−0.9 and Chaplygin gas models with κ≤ 15 at the 3σ level if the value of Ωm is known exactly. The statefinder gives reasonable results even when the value of Ωm is known to only ∼20 per cent accuracy. In this case, marginalizing over Ωm and assuming a fiducial Λ‐cold dark matter (LCDM) model allows us to rule out quintessence with w≥−0.85 and the Chaplygin gas with κ≤ 7 (both at 3σ). These constraints can be made even tighter if we use the statefinders in conjunction with the deceleration parameter. The statefinder is very sensitive to the total pressure exerted by all forms of matter and radiation in the Universe. It can therefore differentiate between dark energy models at moderately high redshifts of z≲ 10.

We reconstruct the equation of state w(z) of dark energy (DE) using a recently released data set containing 172 Type Ia supernovae (SNe) without assuming the prior w(z) ≥−1 (in contrast to previous studies). We find that DE evolves rapidly and metamorphoses from dust‐like behaviour at high z (w≃ 0 at z∼ 1) to a strongly negative equation of state at present (w≲−1 at z≃ 0). DE metamorphosis appears to be a robust phenomenon which manifests for a large variety of SNe data samples provided one does not invoke the weak energy prior ρ+p≥ 0. Invoking this prior considerably weakens the rate of growth of w(z). These results demonstrate that DE with an evolving equation of state provides a compelling alternative to a cosmological constant if data are analysed in a prior‐free manner and the weak energy condition is not imposed by hand.

Abstract. We investigate the behaviour of dark energy using the recently released supernova data of Riess et al., 2004 and a model independent parameterization for dark energy (DE). We find that, if no priors are imposed on Ω 0m and h, DE which evolves with time provides a better fit to the SNe data than ΛCDM. This is also true if we include results from the WMAP CMB data. From a joint analysis of SNe+CMB, the best-fit DE model has w 0 < ∼ − 1 at the present epoch and the transition from deceleration to acceleration occurs at z T = 0.39±0.03. However, DE evolution becomes weaker if the ΛCDM based CMB results Ω 0m = 0.27 ± 0.04, h = 0.71 ± 0.06 are incorporated in the analysis. In this case, z T = 0.57 ± 0.07. Our results also show that the extent of DE evolution is sensitive to the manner in which the supernova data is sampled.

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel in order to reconstruct important cosmological quantities including H(z) and w(z) in a model independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future SuperNova Acceleration Probe (SNAP). We find that the Hubble parameter is especially well-determined and useful for this purpose. The look back time of the universe may also be determined to a very high degree of accuracy ( < ∼ 0.2%) in this method. By refining the method, it is also possible to obtain reasonable bounds on the equation of state of dark energy. We explore a new diagnostic of dark energy-the 'w-probe'-which can be calculated from the first derivative of the data. We find that this diagnostic is reconstructed extremely accurately for different reconstruction methods even if Ω 0m is marginalized over. The w-probe can be used to successfully distinguish between ΛCDM and other models of dark energy to a high degree of accuracy.