On Second-order Perturbation Theories of Gravitational Instability in Friedmann-Lemaitre Models

Details On Second-order Perturbation Theories of Gravitational Instability in Friedmann-Lemaitre Models On Second-order Perturbation Theories of Gravitational Instability in Friedmann-Lemaitre Models

1995-10-26

arxiv.org/abs/astro-ph/9510137v1

Prog.Theor.Phys. 94 (1995) 1151-1156

Astronomy and Astrophysics

Astrophysics

9 pages, LaTeX, to appear in Progress of Theoretical Physics (Letters)

Scientific paper

10.1143/PTP.94.1151

The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in $\Omega \neq 1$ and $\Lambda \neq 0$ {}Friedmann-Lema\^{\i}tre models. I explicitly write the second-order theories in terms of closed one-dimensional integrals. In cosmologically interested cases ($\Lambda = 0$ or $\Omega + \lambda = 1$), they reduce to elementary functions or hypergeometric functions. For arbitrary $\Omega$ and $\Lambda$, I present accurate fitting formula which are sufficient in practice for the observational cosmology. It is reconfirmed for generic $\Omega$ and $\Lambda$ of interest that second-order effect only weakly depends on these parameters.

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