Exploring the expanding Universe and dark energy using the statefinder diagnostic

Abstract

The coming few years are likely to witness a dramatic increase in high‐quality supernova data as current surveys add more high‐redshift supernovae to their inventory and as newer and deeper supernova experiments become operational. Given the current variety in dark energy models and the expected improvement in observational data, an accurate and versatile diagnostic of dark energy is the need of the hour. This paper examines the statefinder diagnostic in the light of the proposed SuperNova Acceleration Probe (SNAP) satellite, which is expected to observe about 2000 supernovae per year. We show that the statefinder is versatile enough to differentiate between dark energy models as varied as the cosmological constant on one hand, and quintessence, the Chaplygin gas and braneworld models, on the other. Using SNAP data, the statefinder can distinguish a cosmological constant (w=−1) from quintessence models with w≥−0.9 and Chaplygin gas models with κ≤ 15 at the 3σ level if the value of Ωm is known exactly. The statefinder gives reasonable results even when the value of Ωm is known to only ∼20 per cent accuracy. In this case, marginalizing over Ωm and assuming a fiducial Λ‐cold dark matter (LCDM) model allows us to rule out quintessence with w≥−0.85 and the Chaplygin gas with κ≤ 7 (both at 3σ). These constraints can be made even tighter if we use the statefinders in conjunction with the deceleration parameter. The statefinder is very sensitive to the total pressure exerted by all forms of matter and radiation in the Universe. It can therefore differentiate between dark energy models at moderately high redshifts of z≲ 10.

Dark Energy

“…A simple polynomial fit to f (z) was proposed by Alam et al [763], which is a truncated Taylor expansion f (z) = A 0 + A 1 (1 + z) + A 2 (1 + z) 2 .…”

Statefinder revisited

“…Comparing figures 10 and 13 we could say, as suggested by Alam et al [3], that the pair {q,s} is even a better diagnostic than {r,s}, once it restricts the area of the phase space filled by the data. However, if there is a systematic error present, the points will be shifted to the negative direction of the q axis only (figure 15), letting the distance between the data and the fiducial model bigger than those in figure 12.…”

“…Next, we investigated the integrated averaged of the cosmological parameters, as suggested by Alam et al [3]. For the cosmological constant model, the parameters are constant, but for many dark energy models the statefinder evolves (as it is clear in the figures presented previously), the integration of this quantities may then reduce the noise in the original data.…”

Statefinder Diagnosis for the Extended Holographic Ricci Dark Energy Model without and with Interaction

“…An approach is claimed to differentiate between them. As is well known, the statefinder is a sensitive and robust geometrical diagnostic of dark energy, which is constructed using both the second and third derivatives of the scale factor a(t) [27,28]. Let us consider the general form for the scale factor of the universe…”