Abstract
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 for the present Gaussian curvature of three-space. They integrate the Friedmann equation numerically, requiring solutions to match the present Hubble parameter and mass-density ("closure") parameter at present time , and generate families of curves showing the scale factor (with ) vs (time in units ) for fixed and various values of the cosmological constant (in units ). These unusual graphs show the continuity of the solutions and the physical significance of . Families for several values of exhibit known but unfamiliar features. The authors also show the family of "standard models" () and the family satisfying the "inflationary constraint" (). They obtain new and simple formulas for the critical value , which separates models with a big bang from those without. Their definition of at fixed and differs from usual practice but proves useful. These formulas also give the quasistatic scale factor and redshift for the corresponding Eddington-Lemaître model, and give and approximately for the neighboring "Lemaître coasting models," which have . The conventional wisdom that for the coasting models applies to a different characteristic value . A quasistatic state in the future, with a second critical value , is possible if . The parameters , , , and can be used to classify the Friedmann models.
DOI:https://doi.org/10.1103/RevModPhys.58.689
©1986 American Physical Society