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

The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in Ω≠1 and Λ≠0 Friedmann-Lemaître models. We explicitly write the second-order theories in terms of closed one-dimensional integrals. In cosmologically interested cases (Λ= 0 or Ω+ λ= 1), they reduce to elementary functions or hypergeometric functions. For arbitrary Ω and Λ. We present accurate fitting formula which is sufficient in practice for the observational cosmology. It is reconfirmed for generic Ω and Λ of interest that second-order effect only weakly depends on these parameters.