SLAC-PUB-10814 astro-ph/0408279

Our fundamental lack of understanding of the acceleration of the Universe suggests that we consider a kinematic description. The simplest formalism involves the third derivative of the scale factor through a jerk parameter. A new approach is presented for describing the results of astronomical observations in terms of the contemporary jerk parameter and this is related to the equation of state approach. Simple perturbative expansions about ΛCDM are given. 1. Approaches to Dark Energy The Universe is spatially flat, accelerating and has a subcritical matter density. The evidence for this comes from: • observation of acoustic peaks in the microwave background radiation spectrum which effectively measures the angular diameter distance dA to the last scattering surface (e.g. Spergel et al. 2003). • magnitudes of Type Ia supernovae which provide the luminosity distance dL as a function of redshift (e.g. Riess et al. 2001). • X-ray observations of rich clusters of galaxies which measure the mean density of dark matter and also, with less confidence, the distance–redshift relation (e.g. Allen et al. 2004). Although the possibility that the Universe contains a repulsive entity counteracting the attractive effects of gravity was entertained by Einstein in the first, relativistic cosmology, the discovery of acceleration was mostly a surprise. There have been several approaches to rationalizing this discovery from a contemporary perspective. The simplest, and probably still the favorite description, is that the field equation is supplemented by a term proportional to the metric tensor, which guarantees covariance. The coefficient of proportionality (the cosmological constant) is the single free parameter in the theory. If we regard this term as an augmentation of the stress energy tensor of cold matter and adopt a fluid description, then the enthalpy must vanish and the pressure is the negative of the energy density (roughly 0.7 nJ m−3). Alternatively, we can regard this term as a necessary component of the geometrical response of a spacetime manifold to a material source that only becomes detectable on cosmological scales. Either choice leads to the flat “ΛCDM” cosmology in which the cosmic time varies with the scale factor a = 1/(1 + z) according to the SLAC-PUB-10814 astro-ph/0408279 October 2004 Work supported in part by the Department of Energy Contract DE-AC02-76SF00515 Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Presented at NOAO Workshop on Observing Dark Energy, 3/18/2004 3/20/2004, Tucson, AZ, USA