The Cold Dark Matter Density Perturbation

TL;DR

This review analyzes how inflation-generated, adiabatic density perturbations within a cold dark matter framework seed structure formation and imprint the cosmic microwave background. It presents a coherent perturbation theory (via Hawking's fluid-flow approach), derives the transfer function, and connects primordial spectra to observables like COBE and galaxy surveys, including the role of gravitational waves. The authors explore inflationary model predictions for the spectral tilt n and tensor contributions, and critically assess CDM against a range of data, arguing that pure CDM struggles to fit all observations; extensions such as tilt, cosmological constant, and mixed hot+cold dark matter are considered as viable alternatives. The work underscores the importance of linking microphysical inflationary parameters to large-scale structure and CMB measurements, guiding subsequent refinements in cosmological models.

Abstract

This is a review of the Cold Dark Matter model of structure formation, and its variants. The approach is largely from first principles, the main aim being to impart a basic understanding of the relevant theory with an eye to the likely intense activity of the next few years, but the current observational status of the model is also critically assessed. The evolution of adiabatic and isocurvature density perturbations is described, and their effect on the large scale cmb anisotropy calculated as well as that of any gravitational waves. The generation of all three types of perturbation during inflation is described, and the normalisation and spectral indices are calculated in terms of the inflationary potential and its first and second derivatives. The comparison of the theory with each type of observation is described, starting with the COBE data and moving down in scale to the non-linear regime. Constraints on the spectrum of the adiabatic density perturbation are exhibited, the spectrum being parametrised by its normalisation and its degree of tilt. Finally extensions of the CDM model are considered, which replace some of the cold dark matter by hot dark matter or a cosmological constant.