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.

Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter w(z) will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for w(z). We introduce a new, nonparametric method for solving the associated statistical inverse problem based on Gaussian process modeling and Markov chain Monte Carlo sampling. Applying this method to recent supernova measurements, we reconstruct the continuous history of w out to redshift z=1.5.

A basic aim of ongoing and upcoming cosmological surveys is to unravel the mystery of dark energy. In the absence of a compelling theory to test, a natural approach is to better characterize the properties of dark energy in search of clues that can lead to a more fundamental understanding. One way to view this characterization is the improved determination of the redshift-dependence of the dark energy equation of state parameter, w(z). To do this requires a robust and bias-free method for reconstructing w(z) from data that does not rely on restrictive expansion schemes or assumed functional forms for w(z). We present a new nonparametric reconstruction method that solves for w(z) as a statistical inverse problem, based on a Gaussian Process representation. This method reliably captures nontrivial behavior of w(z) and provides controlled error bounds. We demonstrate the power of the method on different sets of simulated supernova data; the approach can be easily extended to include diverse cosmological probes. 95.36.+x

We reconstruct dark energy properties from two complementary supernova datasets -the newly released Gold+HST sample and SNLS. The results obtained are consistent with standard ΛCDM model within 2σ error bars although the Gold+HST data favour evolving dark energy slightly more than SNLS. Using complementary data from baryon acoustic oscillations and the cosmic microwave background to constrain dark energy, we find that our results in this case are strongly dependent on the present value of the matter density Ω0m. Consequently, no firm conclusions regarding constancy or variability of dark energy density can be drawn from these data alone unless the value of Ω0m is known to an accuracy of a few percent. However, possible variability is significantly restricted if this data is used in conjunction with supernova data. INTRODUCTIONThere is a growing consensus in cosmology that the Universe is currently accelerating. Perhaps the simplest explanation of this property is the presence of a positive cosmological constant Λ. Although Λ appears to explain all current observations satisfactorily, to do so its value must necessarily be very small Λ/8πG ≃ 10 −47 GeV 4 . So, it represents a new small constant of nature in addition to those known from elementary particle physics. However, since it is not known at present how to derive it from these other small constants and it is even unclear if it should be exactly constant, other phenomenological explanations for cosmic acceleration have been suggested. Collectively called dark energy (DE) models, they are based either on the introduction of new physical fields (quintessence and phantom models, the Chaplygin gas, etc.), or on geometrical approaches which attempt to generate acceleration by means of a change in the laws of gravity and, therefore, the geometry of space-time [1]. Scalar-tensor gravity, R+ f (R) gravity and higher dimensional 'Braneworld' models are prominent members of this second category.The growing number of DE models has inspired a complementary approach whose aim is to reconstruct properties of DE directly from observations in a quasi-model independent manner, see the recent review [2] and the extensive list of references therein. The aim of this paper is to investigate what new insights can be obtained about DE using the most recent data, and to see whether or not these data strengthen previously obtained results on the closeness of DE to Λ. We study two different supernova samples -the newly released Gold+HST sample [3] and SNLS data [4] to see what constraints follow from them on possible evolution of DE. We also investigate the possibility of extracting information about the nature of DE from datasets other than the supernova data. To this end, we consider what follows from the value of the R parameter characterizing acoustic peaks in the angular power spectrum of the cosmic microwave background (CMB) [5,6] and from the SDSS result on the baryon acoustic oscillation peak (BAO) [7]. DATA AND METHODOLOGYIn this paper, we shall compare the reconstruction re...