NONLINEAR STRUCTURE FORMATION IN FLAT COSMOLOGICAL MODELS

This paper describes the formation of nonlinear structure in flat (zer o curvature) Friedmann cosmological models. We consider models with tw o components: the usual nonrelativistic component that evolves under g ravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not dump 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 p arameters: the exponent n and the present density parameter Omega(0) o f the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n > 3, and n < 3. The case n = 3 is relevant to models with massi ve neutrinos. The presence of the uniform component strongly reduces t he growth of the perturbation compared with the Einstein-de Sitter mod el. We show that the Meszaros effect (suppression of growth at high re dshift) holds not only for n = 4, radiation-dominated models, but for all models with n > 3. This essentially rules out any such model. For the case n < 3, we numerically integrate the perturbation equations fr om the big bang to the present, for 620 different models with various values of Omega(0) and n. Using these solutions, we show that the func tion f(Omega(0), n)= (a/delta(+))d delta(+)/da, which enters in the re lationship between the present density contrast delta(0) and peculiar velocity field u(0), is essentially independent of n. We derive approx imate solutions for the second-order perturbation equations. These sec ond-order solutions are tested against the exact solutions and the Zel 'dovich approximation for spherically symmetric perturbations in the m arginally nonlinear regime (\delta\ less than or similar to 1). The se cond order and Zel'dovich solutions have comparable accuracy, signific antly higher than the accuracy of the linear solutions. We then invest igate the dependence of the delta(0) - u(0) relationship upon the valu e of n in the nonlinear regime using the second-order solutions for ma rginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both case s, we find that the delta(0) - u(0) relationship remains independent o f n. We speculate that this result extends to strongly nonlinear, gene ral perturbations as well. This eliminates any hope to determine the p resence of the uniform component or the value of n using dynamical met hods. Finally, we compute the nonlinear evolution of the skewness of t he distribution of values of delta, assuming Gaussian initial conditio ns. We find that the skewness is not only independent of n, but also o f Omega(0). Thus the skewness cannot be used to discriminate among var ious models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We c onclude that the uniform component leaves no observable signature in t he present large-scale structure of the universe. To determine its pre sence and nature, we must investigate the relationship between the pas t and present universe, using redshift-dependent tests.