2ND-ORDER POWER SPECTRUM AND NONLINEAR EVOLUTION AT HIGH-REDSHIFT

The Eulerian cosmological fluid equations are used to study the nonlin ear mode coupling of density fluctuations. We evaluate the second-orde r power spectrum including all four-point contributions. In the weakly nonlinear regime we find that the dominant nonlinear contribution for realistic cosmological spectra is made by the coupling of long-wave m odes and is well estimated by second-order perturbation theory. For a linear spectrum like that of the cold dark matter model, second-order effects cause a significant enhancement of the high-k part of the spec trum and a slight suppression at low k near the peak of the spectrum. Our perturbative results agree well in the quasi-linear regime with th e nonlinear spectrum from high-resolution N-body simulations. We find that due to the long-wave mode coupling, characteristic nonlinear mass es grow less slowly in time (i.e., are larger at higher redshifts) tha n would be estimated using the linear power spectrum. For the cold dar k matter model at (I + z) = (20, 10, 5, 2) the nonlinear mass is about (180, 8, 2.5, 1.6) times (respectively) larger than a linear extrapol ation would indicate, if the condition rms deltarho/rho = 1 is used to define the nonlinear scale. At high redshift the Press-Schechter mass distribution significantly underestimates the abundance of high-mass objects for the cold dark matter model. Although the quantitative resu lts depend on the definition of the nonlinear scale, these basic conse quences hold for any initial spectrum whose postrecombination spectral index n decreases sufficiently rapidly with increasing k, a feature t hat arises quite generally during the transition from a radiation- to matter-dominated universe.