Nonlinear cosmological power spectra in real and redshift space
Abstract
We present an expression for the nonlinear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in selfgravitating fields. Some exact solutions are found for powerlaw initial spectra. We have extended this analysis into redshift space and found a solution for the nonlinear, anisotropic redshiftspace power spectrum in the limit of planeparallel redshift distortions. The quadrupoletomonopole ratio is calculated for the case of powerlaw initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshiftspace distortion parameter, beta. The point of zerocrossing of the quadrupole, k_0, is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of Nbody simulations on scales down to the zerocrossing of the quadrupole, although the wavenumber at zerocrossing is underestimated. These results are applied to the quadrupoletomonopole ratio found in the merged QDOT plus 1.2Jy IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta>0.5 at the 95 per cent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n~2 in the translinear regime. The zerocrossing scale of the quadrupole is k_0=0. 5+/0.1h Mpc^1 and from this we infer that the amplitude of clustering is sigma_8=0.7+/0.05. We suggest that the success of this model is due to nonlinear redshiftspace effects arising from infall on to caustics and is not dominated by virialized cluster cores. The latter should start to dominate on scales below the zerocrossing of the quadrupole, where our model breaks down.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 October 1996
 DOI:
 10.1093/mnras/282.3.767
 arXiv:
 arXiv:astroph/9604020
 Bibcode:
 1996MNRAS.282..767T
 Keywords:

 COSMOLOGY;
 THEORY  LARGESCALE STRUCTURE OF UNIVERSE;
 Astrophysics
 EPrint:
 13 pages, uufiles, Latex with 6 postscript figures, submitted to MNRAS