Integration of the Friedmann equation for universes of arbitrary complexity
Abstract
An explicit and complete set of constants of the motion are constructed algorithmically for FriedmannLemaîtreRobertsonWalker (FLRW) models consisting of an arbitrary number of noninteracting species, each with a constant ratio of pressure to density. 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 a unique candidate for a gravitational epoch function—a function which gives a global timeorientation without reference to observers. 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 ΛCDM model, it is shown that the epoch function exists for all models with Λ>0, but for almost no models with Λ<0.
 Publication:

Physical Review D
 Pub Date:
 December 2006
 DOI:
 10.1103/PhysRevD.74.123505
 arXiv:
 arXiv:grqc/0603028
 Bibcode:
 2006PhRvD..74l3505L
 Keywords:

 98.80.Jk;
 04.20.Cv;
 04.40.b;
 Mathematical and relativistic aspects of cosmology;
 Fundamental problems and general formalism;
 Selfgravitating systems;
 continuous media and classical fields in curved spacetime;
 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Theory
 EPrint:
 Final form to appear in Physical Review D15