A kinematical approach to dark energy studies

Abstract

We present and employ a new kinematical approach to cosmological `dark energy' studies. We construct models in terms of the dimensionless second and third derivatives of the scalefactor a(t) with respect to cosmic time t, namely the present-day value of the deceleration parameter q<sub>0</sub> and the cosmic jerk parameter, j(t). An elegant feature of this parametrization is that all Λ cold dark matter (ΛCDM) models have j(t) = 1 (constant), which facilitates simple tests for departures from the ΛCDM paradigm. Applying our model to the three best available sets of redshift-independent distance measurements, from Type Ia supernova and X-ray cluster gas mass fraction measurements, we obtain clear statistical evidence for a late-time transition from a decelerating to an accelerating phase. For a flat model with constant jerk, j(t) = j, we measure q<sub>0</sub> = -0.81 +/- 0.14 and j = 2.16<sup>+0.81</sup><sub>-0.75</sub>, results that are consistent with ΛCDM at about the 1σ confidence level. A standard `dynamical' analysis of the same data, employing the Friedmann equations and modelling the dark energy as a fluid with an equation-of-state parameter, w (constant), gives Ω_m = 0.306^+0.042_-0.040 and w = -1.15^+0.14_-0.18, also consistent with ΛCDM at about the 1σ level. In comparison to dynamical analyses, the kinematical approach uses a different model set and employs a minimum of prior information, being independent of any particular gravity theory. The results obtained with this new approach therefore provide important additional information and we argue that both kinematical and dynamical techniques should be employed in future dark energy studies, where possible. Our results provide further interesting support for the concordance ΛCDM paradigm.