Statefinder—A new geometrical diagnostic of dark energy

We introduce a new cosmological diagnostic pair {r, s} called the Statefinder. The Statefinder is a geometrical diagnostic and allows us to characterize the properties of dark energy in a model-independent manner. The Statefinder is dimensionless and is constructed from the scale factor of the Universe and its time derivatives only. The parameter r forms the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter H and the deceleration parameter q, while a is a linear combination of q and r chosen in such a way that it does not depend upon the dark energy density. The Statefinder pair {r, s} is algebraically related to the equation of state of dark energy and its first time…