A phase-space representation of Friedmann-Lemaitre universes containing both dust and radiation and the inevitability of a big bang

Details A phase-space representation of Friedmann-Lemaitre universes containing both dust and radiation and the inevitability of a big bang A phase-space representation of Friedmann-Lemaitre universes containing both dust and radiation and the inevitability of a big bang

May 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989mnras.238..503e&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 238, May 15, 1989, p. 503-521.

Mathematics

Logic

28

Background Radiation, Big Bang Cosmology, Cosmic Dust, Red Shift, Flux Density, Universe

Scientific paper

We classify all non-static Friedmann-Lemaître universes containing dust and radiation (or, as limiting cases, vacuum), and exhibit their histories as orbits in a three-dimensional (phase-) space ℘, which faithfully reflects the topology of the set of states. As coordinates in ℘ we take the dimensionless parameters Ω, ω and λ representing, respectively, the energy density of the dust, the radiation and the vacuum (corresponding to the cosmological constant). Three open subspaces of ℘ contain, respectively, the orbits representing oscillating, inflectional and bouncing universes; their boundaries and edges contain the orbits of all the other universes. The classification proceeds from initial values (Ω0,ω0) in terms of (α, λ0) diagrams (α = R/R0). An alternative set of `invariant' parameters is also introduced, characterizing whole models rather than states of models. Finally we show that present-day redshift and density data exclude all models not having a big bang, without using assumptions about the origin of the microwave background radiation and without a priori assumptions about the value of the cosmological constant.

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