Exploring the expanding Universe and dark energy using the statefinder diagnostic

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 (omega = -1) from quintessence models with omega greater than or equal to -0.9 and Chaplygin gas models with kappa less than or equal to 15 at the 3sigma level if the value of Omega(m) is known exactly. The statefinder gives reasonable results even when the value of Omega(m) is known to only similar to20 per cent accuracy. In this case, marginalizing over Omega(m) and assuming a fiducial Lambda-cold dark matter (LCDM) model allows us to rule out quintessence with omega greater than or equal to -0.85 and the Chaplygin gas with kappa less than or equal to 7 (both at 3sigma). 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 less than or similar to 10.