Statefinder—A new geometrical diagnostic of dark energy

By V. Sahni, T. D. Saini, A. Starobinsky, Ujjaini Alam. 2002

1,320 citations recorded by the source corpus.

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 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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/faca12ceb91ca9005282335cb0220e5c3a5eba65

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In Astronomy and Astrophysics

1. Xin Zhang
2. A. Starobinsky
3. Yi Wang
4. Shuang Wang
5. V. Sahni
6. Miao Li
7. A. Shafieloo
8. Ujjaini Alam

Citations in the corpus

• Exploring the expanding Universe and dark energy using the statefinder diagnostic (2003, methodology): “Then such a sensitive diagnostic of the present acceleration epoch and of dark energy could be the statefinder pair {r, s}, recently introduced in Sahni et al. (2003).”
• A kinematical approach to dark energy studies (2006, background): “We note that Sahni et al. (2003) and Alam et al. (2003) also drew attention to the importance of the jerk parameter for discriminating models of dark energy and/or modified gravity.”
• MODEL-INDEPENDENT EVIDENCE FOR DARK ENERGY EVOLUTION FROM BARYON ACOUSTIC OSCILLATIONS (2014, background): “One such diagnostic is the Statefinder r = ...a /aH 3 (also called the jerk) whose value remains at unity only in ΛCDM (Sahni et al. 2003; Alam et al. 2003) (also see Chiba & Nakamura 1998; Visser 2004).”
• CAN THE CHAPLYGIN GAS BE A PLAUSIBLE MODEL FOR DARK ENERGY (2002, methodology): “To begin with, let us rewrite the formulae for the statefinder parameters [ 1 ] in a form convenient for our purposes.”
• Statefinder diagnosis for the interacting model of holographic dark energy (2007, background): “The spatially flat LCDM (cosmological constant λ with cold dark matter) scenario corresponds to a fixed point in the diagram {s, r} ∣ ∣ ∣ ∣ LCDM = {0, 1} .”
• Holographic dark energy (2016, background): “A most famous geometrical diagnostic is the so-called “statefinder” pair {r, s} [237], defined as r ≡ .”
• Jerk, snap, and the cosmological equation of state (2003, neutral): “Dated: 24 March 2004; LATEX-ed 24 March 2022 PACS numbers: gr-qc/0309109”