The Effective Field Theory and Perturbative Analysis for Log-Density
  Fields
  A logarithm transformation over the matter overdensity field $\delta$ 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 $\delta$ 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 \simeq 0.38 $
Mpc$^{-1}$h 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.
