3.4. Probing dark energy using the Statefinder statistic

An issue of the utmost importance is whether dark energy (equivalently quintessence) is a cosmological constant or whether it has a fundamentally different origin. A new dimensionless statistic `Statefinder', recently introduced by Sahni, Saini, Starobinsky and Alam [53] has the power to discriminate between different forms of dark energy and may therefore be a good diagnostic of cosmological models.

The Statefinder pair {r, s} is constructed from the scale factor of the universe and its derivatives and probes the cosmic equation of state and its rate of change. It extends the hierarchy of geometrical cosmological parameters to four: {H, q, r, s}, where H = ( / a), q = -H-2( / a),

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From figure 5 we see that while r remains fixed at r = 1 in a universe containing matter and a cosmological constant, the value of r decreases steadily for time varying forms of dark energy. The Statefinder statistic can therefore help differentiate a cosmological constant from: (i) dark energy with a time-independent equation of state (referred to in [53] as Quiessence) and (ii) dark energy with a time-dependent equation of state (referred to in [53] as Kinessence).

 Figure 5. The Statefinder pair {r, s} is shown for dark energy consisting of a cosmological constant , Quiessence `Q' with an unevolving equation of state w = - 0.8 and the inverse power law tracker model V = V0 / 2, referred to as Kinessence `K'. The lower left panel shows r(z) while the lower right panel shows s(z). Kinessence has a time-dependent equation of state which is shown in the top right panel. The fractional density in matter and Kinessence is shown in the top left panel. The ability of the Statefinder pair {r, s} to differentiate between the different forms of dark energy is amply demonstrated by this figure which is reproduced from Sahni, Saini, Starobinsky and Alam [53].