Second-order perturbation theory in Omega is not equal to Friedmann models

Abstract

view Abstract Citations (35) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Second-Order Perturbation Theory in Omega not = 1 Friedmann Models Martel, Hugo ; Freudling, Wolfram Abstract This paper presents approximate second-order (quadratic) solutions for the density contrast and peculiar velocity field in Friedmann models with arbitrary density parameter Omega. It shows that the second-order perturbation equations are solvable if one can replace Omega exp 1.2 by Omega in one of the terms. These solutions are tested against exact solutions for spherical and sinusoidal perturbations, and comparisons with linear theory and with the Zel'dovich approximation are made. The quadratic solutions for the density contrast constitute a major improvement over the results of linear theory. That is not necessarily the case for the peculiar velocity field, as one must be very careful with the boundary conditions. The quadratic solutions and the Zel'dovich approximation are found to have similar accuracy. The applicability of these two different methods to concrete problems is discussed. Publication: The Astrophysical Journal Pub Date: April 1991 DOI: 10.1086/169864 Bibcode: 1991ApJ...371....1M Keywords: Astronomical Models; Computational Astrophysics; Cosmology; Perturbation Theory; Boundary Conditions; Density Distribution; Velocity Distribution; Astrophysics; COSMOLOGY full text sources ADS |