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 scale factor a(t) with respect to cosmic time t, namely the present-day value of the deceleration parameter q_0 and the cosmic jerk parameter, j(t). An elegant feature of this parameterization is that all LCDM models have j(t)=1 (constant), which facilitates simple tests for departures from the LCDM paradigm. Applying our model to the three best available sets of redshift-independent distance measurements, from type Ia supernovae 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_0=-0.81+-0.14 and j=2.16+0.81-0.75, results that are consistent with LCDM at about the 1sigma confidence level. A standard `dynamical' analysis of the same data, employing the Friedmann equations and modeling the dark energy as a fluid with an equation of state parameter, w (constant), gives Omega_m=0.306+0.042-0.040 and w=-1.15+0.14-0.18, also consistent with LCDM at about the 1sigma 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 LCDM paradigm.Comment: 12 pages, 5 figures, 2 tables. Accepted for publication in MNRA

Probing the cosmographic parameters to distinguish between dark energy and modified gravity models

“…The observations of the spectrum of cosmic microwave background (CMB) anisotropies (Spergel et al 2003(Spergel et al , 2007, large-scale structure (LSS) (Tegmark et al 2004;Eisenstein et al 2005) and the distance-redshift relation to X-ray galaxy clusters (Allen et al 2004(Allen et al , 2007) also confirm that the universe is accelerating. Possible explanations for this acceleration have been proposed.…”

“…Visser (2004) expanded the Hubble law to fourth order in redshift including the snap parameter and put constraints on the deceleration and jerk parameters using SNe Ia (Visser 2004). Rapetti et al (2007) constrained the deceleration and jerk parameters from SNe Ia and X-ray cluster gas mass fraction measurements. For a redshift range of SNe Ia, the terms beyond the cubic power of the Hubble law can be neglected.…”

Scalar field deformations ofΛCDMcosmology

“…(11), and below we will also express H in state space variables. In addition it is of interest to give the jerk parameter j [16,17], since even though the observational feasibility of j is questionable, it is still useful in order to theoretically compare models with ΛCDM cosmology for which j = 1; for constant γ m the jerk parameter is given by…”

“…Here the cosmographic (or cosmokinetic) quantities a(t), H(t), q(t), j(t) are the cosmological scale factor and the time-dependent Hubble, deceleration, and jerk parameters, respectively [16,17], which take the following form for the ΛCDM models:…”

How well can the evolution of the scale factor be reconstructed by the current data?

“…Different approaches have been used in the literature in order to reconstruct some kinematic quantities such as the luminosity distance D L (z), H(z), q(z) and the jerk 220 S. Vitenti & M. Penna-Lima function. One of these methods assumes a priori a functional form of the scale factor H(z) and so on (Riess et al 2004, Visser 2004, Rapetti et al 2007, Lu et al 2011, Shafieloo 2012. This parametric reconstruction is strongly model dependent, so, besides having small variances the results present large biases.…”