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Statefinder: A New geometrical diagnostic of dark energy

Varun Sahni
(
- IUCAA, Pune
)
,
Tarun Deep Saini
(
- IUCAA, Pune
)
,
Alexei A. Starobinsky
(
- Landau Inst.
)
,
Ujjaini Alam
(
- IUCAA, Pune
)

Jan, 2002

6 pages

Published in:

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

e-Print:

astro-ph/0201498 [astro-ph]

DOI:

10.1134/1.1574831

View in:

ADS Abstract Service

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Abstract: (arXiv)

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.

Note:

7 pages, 3 figures. Final version to be published in JETP Lett., presentation shortened, references added and updated, consideration of brane cosmological models included, conclusions unchanged

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