Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-03-09
Phys.Rev.D74:123505,2006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Final form to appear in Physical Review D15
Scientific paper
10.1103/PhysRevD.74.123505
An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of the motion from simpler models as more species are added is stressed. It is then argued that all FLRW models admit what amounts to a unique candidate for a gravitational epoch function (a dimensionless scalar invariant derivable from the Riemann tensor without differentiation which is monotone throughout the evolution of the universe). The same relations that lead to the construction of constants of the motion allow an explicit evaluation of this function. In the simplest of all models, the $\Lambda$CDM model, it is shown that the epoch function exists for all models with $\Lambda > 0$, but for almost no models with $\Lambda \leq 0$.
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