Perturbation Theory of the Cosmological Log-Density Field

International audienceThe matter density field exhibits a nearly lognormal probability densitydistribution (PDF) after entering into the nonlinear regime. Recently, it hasbeen shown that the shape of the power spectrum of a logarithmicallytransformed density field is very close to the linear density power spectrum,motivating an analytic study of it. In this paper, we develop cosmologicalperturbation theory for the power spectrum of this field. Our formalism isdeveloped in the context of renormalized perturbation theory, which helps toregulate the convergence behavior of the perturbation series, and of theTaylor- series expansion we use of the logarithmic mapping. This approachallows us to handle the critical issue of density smoothing in astraightforward way. We also compare our perturbative results with simulationmeasurements