2003/09/30 by Matt Visser · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Relativity and Gravitational Theory #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/21/11/006
published as Class.Quant.Grav.21:2603-2616,2004 · V1: 10 pages; uses iopart.cls setstack.sty V2: six additional references, some clarifying comments and discussion, no physics changes. V3: significant additions based on community feedback; explicit calculations now carried out to fourth order in redshift. V4: Discussion of current observational situation added. This version accepted for publication in Classical and Quantum Gravity. Now 15 pages
arxiv created 2004/03/31 · openalex publication_date 2004/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be 'predictive', in the sense that once some a priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a ( t ). In contrast, a 'retrodictive' approach might usefully take observational data concerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk and snap—the second , third and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak, and are likely to remain weak for the foreseeable future.