COSMOLOGICAL PERTURBATION-THEORY IN THE SYNCHRONOUS AND CONFORMAL NEWTONIAN GAUGES

This paper presents a systematic treatment of the linear theory of sca lar gravitational perturbations in the synchronous gauge and the confo rmal Newtonian (or longitudinal) gauge. It differs from others in the literature in that we give, in both gauges, a complete discussion of a ll particle species that are relevant to any flat cold dark matter (CD M), hot dark matter (HDM), or CDM + HDM models (including a possible c osmological constant). The particles considered include CDM, baryons, photons, massless neutrinos, and massive neutrinos (an HDM candidate), where the CDM and baryons are treated as fluids while a detailed phas e-space description is given to the photons and neutrinos. Particular care is applied to the massive neutrino component, which has been eith er ignored or approximated crudely in previous works. Isentropic initi al conditions on superhorizon scales are derived. The coupled, lineari zed Boltzmann, Einstein, and fluid equations that govern the evolution of the metric and density perturbations are then solved numerically i n both gauges for the standard CDM model and two CDM + HDM models with neutrino mass densities Omega(v) = 0.2 and 0.3, assuming a scale-inva riant, adiabatic spectrum of primordial fluctuations. We also give the full details of the cosmic microwave background anisotropy, and prese nt the first accurate calculations of the angular power spectra in the two CDM + HDM models including photon polarization, higher neutrino m ultipole moments, and helium recombination. The numerical programs for both gauges are available at http://arcturus.mit.edu/cosmics.