Perturbation Theory of the Cosmological Log-Density Field
  The matter density field exhibits a nearly lognormal probability density
distribution (PDF) after entering into the nonlinear regime. Recently, it has
been shown that the shape of the power spectrum of a logarithmically
transformed density field is very close to the linear density power spectrum,
motivating an analytic study of it. In this paper, we develop cosmological
perturbation theory for the power spectrum of this field. Our formalism is
developed in the context of renormalized perturbation theory, which helps to
regulate the convergence behavior of the perturbation series, and of the
Taylor- series expansion we use of the logarithmic mapping. This approach
allows us to handle the critical issue of density smoothing in a
straightforward way. We also compare our perturbative results with simulation
measurements.
