Exploring dark energy using the Statefinder

Observations of high redshift supernovae indicate that the universe is accelerating. The hypothesis of `Dark energy’ (cosmological constant, scalar field tracker potentials, braneworld models, etc.) has been advanced to explain this phenomenon. Sensitive tests of dark energy which can differentiate between rival models are clearly the need of the hour. The statefinder pair $\lbrace r,s\rbrace$isageometricaldiagnosticwhichcanplaythisrole\mathrm{.}$r&s$dependuponthethirdtimederivativeofthescalefactor$\stackrel{…}{a}$ and provide the next logical step in the hierarchy of the cosmological parameter set after $H$ and $q$. The statefinder pair $\{r,s\}$ can be determined to high accuracy from a SNAP type experiment and allows us to successfully differentiate between dark energy models having constant as well as time-varying equations of state.