Relativistic Hierarchical Cosmology. II: Some Classes of Model Universes

Details Relativistic Hierarchical Cosmology. II: Some Classes of Model Universes Relativistic Hierarchical Cosmology. II: Some Classes of Model Universes

Feb 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..32..305w&link_type=abstract

Astrophysics and Space Science, Volume 32, Issue 2, pp.305-314

Astronomy and Astrophysics

Astrophysics

1

Scientific paper

Following the re-expression of the metric for a hierarchical cosmology in Section 1 (Introduction), the metric curvature is considered in Section 2 in showing that the hierarchy models are not, in general, related to the Robertson/Walker models even though the metrics can be made to appear superficially similar. The classes of models examined are quasi-Robertson/Walker models with Λ=0 (Section 3), quasi-Robertson/Walker models with Λ≠0 (Section 4), constant curvature (k(t)=constant) models (Section 5) and zero-curvature (k(t)=0) models (Section 6). The first group have ϱ0αt -3,S(t)αt 2 in a suitable limit; the second group have solutions expressible as incomplete elliptic integrals of the first and third kind; the next group (k(t)=const.) includes an oscillating model withϱ 0 (t)α[sin (t/2T)]-2,S(t)α[sin (t/2T)]2/3 and a model withk(t)αΛ(ϱ 0αt -2), and a model withk(t)αΛ -β 2/3(ϱ 0αe βt , β<0); the last group comprises three models, one having Λ = 0(ϱ 0αt -2), one having Λ=-1/3T 2 where 2πT is the bounce period of the (oscillating) model, and an analogue of the de Sitter Universe with\varrho _0 (t)α e^{ - sqrt {3Λ t} } andS(t)α e^{ - sqrt {(Λ /3)t} } . Section 7 contains our conclusions.

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