Reconstructing the linear power spectrum of cosmological mass fluctuations

TL;DR

This work reconstructs the linear mass power spectrum from multiple galaxy- and cluster-clustering datasets by analytically correcting for nonlinear evolution, redshift-space distortions, and bias under Gaussian initial conditions. The authors extend the HKLM nonlinear mapping to general densities, enabling consistent inversion from nonlinear to linear spectra, and they perform a joint fit across eight datasets to infer $\Omega$ and tracer biases. They find a coherent linear spectrum well described by a zero-baryon CDM transfer function with $\Omega h \approx 0.25$ and a redshift-space distortion scale $\Omega^{0.6}/b_I \approx 1$, with bias ratios across tracers around $b_{\rm A}:b_{\rm R}:b_{ m O}:b_{ m I} \approx 4.5:1.9:1.3:1$. The results align with COBE normalization for a near-scale-invariant spectrum and challenge tilted models with strong gravity-wave components, providing a robust link between large-scale structure observations and underlying cosmological parameters.

Abstract

We describe an attempt to reconstruct the initial conditions for the formation of cosmological large-scale structure. The power spectrum of the primordial fluctuations is affected by bias, nonlinear evolution and redshift-space distortions, but we show how these effects can be corrected for analytically. Using eight independent datasets, we obtain excellent agreement in the estimated linear power spectra given the following conditions. First, the relative bias factors for Abell clusters, radio galaxies, optical galaxies and IRAS galaxies must be in the ratios 4.5:1.9:1.3:1. Second, the data require redshift-space distortion: $Ω^{0.6}/b_{ßI} = 1.0 \pm 0.2$. Third, low values of $Ω$ and bias are disfavoured. The shape of the spectrum is extremely well described by a CDM transfer function with an apparent value of the fitting parameter $Ωh =0.25$. Tilted models predict too little power at 100 Mpc wavelengths.