An extensive investigation of the Generalised Dark Matter model

Abstract

The Cold Dark Matter (CDM) model, wherein the dark matter is treated as a pressureless perfect fluid, provides a good fit to galactic and cosmological data. With the advent of precision cosmology, it should be asked whether this simplest model needs to be extended, and whether doing so could improve our understanding of the properties of dark matter. One established parameterisation for generalising the CDM fluid is the Generalised Dark Matter (GDM) model, in which dark matter is an imperfect fluid with pressure and shear viscosity that fulfill certain closure equations. We investigate these closure equations and the three new parametric functions they contain: the background equation of state w, the speed of sound c_s^2 and the viscosity c_{vis}^2. Taking these functions to be constant parameters, we analyse an exact solution of the perturbed Einstein equations in a GDM-dominated universe and discuss the main effects of the three parameters on the Cosmic Microwave Background (CMB). Our analysis suggests that the CMB alone is not able to distinguish between the GDM sound speed and viscosity parameters, but that other observables, such as the matter power spectrum, are required to break this degeneracy. We also consider other descriptions of imperfect fluids that have a non-perturbative definition and relate these to the GDM model. In particular, we consider scalar fields, an effective field theory (EFT) of fluids, an EFT of Large Scale Structure, non-equilibrium thermodynamics and tightly-coupled fluids. These descriptions could be used to extend the GDM model into the nonlinear regime of structure formation, which is necessary if the wealth of data available on those scales is to be employed in constraining the model. We also derive the initial conditions for adiabatic and isocurvature perturbations and provide the result in a form ready for implementation in Einstein-Boltzmann solvers.