Statefinder - a new geometrical diagnostic of dark energy

V. Sahni, T. D. Saini, A. A. Starobinsky^{+}, U. Alam

Inter-University Centre for Astronomy & Astrophysics, Puné411 007, India

^{+}Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

PACS: 98.80.-k

**Abstract**
We introduce a
new cosmological diagnostic pair called 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
s 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
is algebraically related to the
equation of state of dark energy and its first time derivative.
The Statefinder pair is
calculated for a number of existing models of dark energy having both
constant
and variable w. For the case of a cosmological constant the Statefinder
acquires a particularly simple form.
We demonstrate that the Statefinder diagnostic can
effectively differentiate between different forms of dark energy.
We also show that the
mean Statefinder pair can be determined to very high accuracy from
a SNAP-type experiment.