The effective field theory and perturbative analysis for log-density fields

A logarithm transformation over the matter overdensity field δ brings information from the bispectrum and higher-order n-point functions to the power spectrum. We calculate the power spectrum for the log-transformed field A at one, two and three loops using perturbation theory (PT). We compare the results to simulated data and give evidence that the PT series is asymptotic already on large scales, where the k modes no longer decouple. This motivates us to build an alternative perturbative series for the log-transformed field that is not constructed on top of perturbations of δ but directly over the equations of motion for A itself. This new approach converges faster and better reproduces the large scales at low z. We then show that the large-scale behaviour for the log-transformed field power spectrum can be captured by a small number of free parameters. Finally, we add the counter-terms expected within the effective field theory framework and show that the theoretical model, together with the IR-resummation procedure, agrees with the measured spectrum with percent precision until k ≃ 0.38 Mpc⁻¹h at z=0. It indicates that the non-linear transformation indeed linearizes the density field and, in principle, allows us to access information contained on smaller scales. (paper)