Mathematics – Logic
Scientific paper
Jun 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995apj...445..537m&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 445, no. 2, p. 537-552
Mathematics
Logic
18
Astronomical Models, Background Radiation, Cosmology, Dark Matter, Nonlinearity, Universe, Cosmic Background Explorer Satellite, Flux Density, Gravitational Effects, Perturbation, Skewness
Scientific paper
This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)-n, where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega0 of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega0 and n. Using these solutions, we show that the function f(Omega0, n) = (a/delta+)d(delta)+/da, which enters in the relationship between the present density contrast delta0 and peculiar velocity field u0 is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta0 - u0 relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta0 - u0 relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions.
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