Scale factors R (t) and critical values of the cosmological constant Λ in Friedmann universes

Details Scale factors R (t) and critical values of the cosmological constant Λ in Friedmann universes Scale factors R (t) and critical values of the cosmological constant Λ in Friedmann universes

Jul 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986rvmp...58..689f&link_type=abstract

Reviews of Modern Physics, Volume 58, Issue 3, July 1986, pp.689-698

Physics

74

Scientific paper

The authors review the equations, notational choices, and confusing terminology of the Friedmann (zero-pressure) and Lemaître cosmological models, retaining cgs units as far as practical and in particular retaining units cm-2 for the present Gaussian curvature K0 of three-space. They integrate the Friedmann equation numerically, requiring solutions to match the present Hubble parameter H0 and mass-density ("closure") parameter Ω0 at present time t0=0, and generate families of curves showing the scale factor R (τ) (with R0=1) vs τ (time in units H-10) for fixed Ω0 and various values of the cosmological constant Λ (in units H20). These unusual graphs show the continuity of the solutions and the physical significance of Λ. Families for several values of Ω0 exhibit known but unfamiliar features. The authors also show the family of "standard models" (Λ=0) and the family satisfying the "inflationary constraint" (K0=0). They obtain new and simple formulas for the critical value Λs(H0,Ω0), which separates models with a big bang from those without. Their definition of Λs at fixed H0 and Ω0 differs from usual practice but proves useful. These formulas also give the quasistatic scale factor Rs and redshift zs for the corresponding Eddington-Lemaître model, and give Rs and zs approximately for the neighboring "Lemaître coasting models," which have Λ<Λs. The conventional wisdom that Λ=Λc(1+ɛ) for the coasting models applies to a different characteristic value Λc. A quasistatic state in the future, with a second critical value Λs 2, is possible if Ω0>1. The parameters Ω0, ΛH20, ΛsH20, and Λs 2H20 can be used to classify the Friedmann models.

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