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 Friedmann-Lemaître-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 $\Lambda \le 0$.

arXiv commentFinal form to appear in Physical Review D15

References in corpus (5)

• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• Hubble Space Telescope and Ground-Based Observations of Type Ia Supernovae at Redshift 0.5: Cosmological Implications
• Cosmographic evaluation of deceleration parameter using SNe Ia data
• The flatness problem and $\Lambda$
• A Dynamical Study of the Friedmann Equations

Cited by in corpus (7)

• Adventures in Friedmann Cosmology: An Educationally Detailed Expansion of the Cosmological Friedmann Equations
• An exposition on Friedmann Cosmology with Negative Energy Densities
• Dark matter, and its darkness
• How Problematic is the Near-Euclidean Spatial Geometry of the Large-Scale Universe?
• Testing the LCDM model (and more) with the time evolution of the redshift
• Exact and Perturbed Friedmann-Lemaitre Cosmologies
• A cyclic cosmological model based on the f(ρ) modified theory of gravity