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A phase-space representation of Friedmann-Lemaître universes containing both dust and radiation and the inevitability of a big bang. (English) Zbl 0673.76127

Summary: 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 \({\mathcal S}\), which faithfully reflects the topology of the set of states. As coordinates in \({\mathcal S}\) we take the dimensionless parameters \(\Omega\), \(\omega\) and \(\lambda\) representing, respectively, the energy density of the dust, the radiation and the vacuum (corresponding to the cosmological constant). Three open subspaces of \({\mathcal S}\) 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 \((\Omega_ 0,\omega_ 0)\) in terms of \((a,\lambda_ 0)\) diagrams \((a=R/R_ 0)\). 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.

MSC:

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83F05 Relativistic cosmology
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