Gauge-invariant Density and Temperature Perturbations in the Quasi-Newtonian Formulation

We give an improved formalism for calculating the evolution of densityfluctuations and temperature perturbations in flat universes. Our equations aregeneral enough to treat the perturbations in collisionless relics like massiveneutrinos. We find this formulation to be simpler to use than gauge dependentand other gauge-invariant formalisms. We show how to calculate temperaturefluctuations (including multipole moments) and transfer functions, includingthe case of collisionless relics like massive neutrinos. We call this formalism"quasi-Newtonian" because the equations for the potential and cold matterfluctuation evolution have the same form as the Newtonian gravitationalequations in an expanding space. The density fluctuation variable also has thesame form inside and outside of the horizon which allows the initial conditionsto be specified in a simple intuitive way. Our sample calculations demonstratehow to use these equations in cosmological models which have hot, cold, andmixed dark matter and adiabatic (isentropic) or isocurvature modes. We alsogive an approximation which may be used to get transfer functions quickly.Comment: 1 LaTEX text file (29 pages), and a uuencoded gzip'ed tar file containing 7 Postscript figure