Statefinder -- a new geometrical diagnostic of dark energy

Details Statefinder -- a new geometrical diagnostic of dark energy Statefinder -- a new geometrical diagnostic of dark energy

2002-01-30

arxiv.org/abs/astro-ph/0201498v2

JETP Lett.77:201-206,2003; Pisma Zh.Eksp.Teor.Fiz.77:249-253,2003

Astronomy and Astrophysics

Astrophysics

7 pages, 3 figures. Final version to be published in JETP Lett., presentation shortened, references added and updated, conside

Scientific paper

10.1134/1.1574831

We introduce a new cosmological diagnostic pair $\lbrace r,s\rbrace$ 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 $\Omega_X(z)$. The Statefinder pair $\lbrace r,s\rbrace$ is algebraically related to the the dark energy pressure-to-energy ratio $w=p/\epsilon$ 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.

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