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.

Observations of high-redshift type Ia supernovae indicate that the universe is accelerating, fueled perhaps by a cosmological constant or by a self-interacting scalar field. In this letter, we develop a model-independent method for estimating the form of the scalar field potential V (φ) and the associated equation of state w φ ≡ p/ε φ . Our method is based on a simple yet powerful analytical form for the luminosity distance DL which is optimized to fit observed distances to distant extragalactic supernovae, and then differentiated to yield V (φ) and w φ . Our results favor w φ −1 at the present epoch, steadily increasing with redshift. However, a cosmological constant is consistent with our results. A model-independent way of obtaining the age of the universe is also proposed.PACS numbers: 98.80. Es, 98.80.Cq, 98.80.Hw, 97.60.Bw The relation between luminosity distance and redshift for extragalactic Type Ia Supernovae (SNe) appears to favor an accelerating Universe, where almost two-thirds of the critical energy density may be in the form of a component with negative pressure [1,2]. On the other hand, several studies of large-scale structure, including those of the abundances of rich galaxy clusters [3] and clustering of galaxies [4] and Lyman-α clouds [5] (for recent reviews, see [6]) indicate low baryonic and matterThis consistency is encouraging since it is well-known that a flat Cold Dark matter Universe with Ω M < 1 and a Cosmological Constant Λ > 0 fits observations of large-scale structure [6,7] better than any other theoretical model.Although Λ = 0 does agree well with the recent SNe observations, it is clear that at a theoretical level a constant Λ runs into serious difficulties, since the present value of Λ is ∼10 123 times smaller than predicted by most particle physics models [7].A time-dependent Λ-like term, which considerably alleviates this fine-tuning problem, can be described in a simple and natural way in terms of a scalar field (referred to here as the Λ-field) with a self-interaction potential V (φ) which is minimally coupled to the Einstein gravity field, and has little or no coupling to any other known physical field. Actually, this model mimics the simplest variant of the inflationary scenario of the early Universe. Since we have not yet got a definite prediction for the form of V (φ) from theoretical considerations, it has to be reconstructed from present-day observations.The aim of the present letter is to go from observations to theory, i.e. from D L (z) to V (φ), following the prescription outlined by Starobinsky [8] (see also [9]). This is the first attempt at reconstructing V (φ) from real observational data without resorting to specific models (e.g. cosmological constant, quintessence etc.).Since the spatially flat Universe (Ω φ + Ω M = 1) is both predicted by the simplest inflationary models and agrees well with observational evidence, we will not consider spatially curved Friedmann-Robertson-Walker (FRW) cosmological models. In a flat FRW cosmology, the luminosity distance D L ...

We examine the behavior of an anisotropic brane-world in the presence of inflationary scalar fields. We show that, contrary to naive expectations, a large anisotropy does not adversely affect inflation. On the contrary, a large initial anisotropy introduces more damping into the scalar field equation of motion, resulting in greater inflation. The rapid decay of anisotropy in the brane-world significantly increases the class of initial conditions from which the observed universe could have originated. This generalizes a similar result in general relativity. A unique feature of Bianchi I brane-world cosmology appears to be that for scalar fields with a large kinetic term the initial expansion of the universe is quasi-isotropic. The universe grows more anisotropic during an intermediate transient regime until anisotropy finally disappears during inflationary expansion.98.90.Cq 04.50.+h