  We propose a new method to linearise cosmological mass density fields using
higher order Lagrangian perturbation theory (LPT). We demonstrate that a given
density field can be expressed as the sum of a linear and a nonlinear component
which are tightly coupled to each other by the tidal field tensor within the
LPT framework. The linear component corresponds to the initial density field in
Eulerian coordinates, and its mean relation with the total field can be
approximated by a logarithm (giving theoretical support to recent attempts to
find such component). We also propose to use a combination of the linearisation
method and the continuity equation to find the mapping between Eulerian and
Lagrangian coordinates. In addition, we note that this method opens the
possibility of use directly higher order LPT on nonlinear fields. We test our
linearization scheme by applying it to the z~0.5 density field from an N-body
simulation. We find that the linearised version of the full density field can
be successfully recovered on >~5 h^{-1}Mpc, reducing the skewness and kurtosis
of the distribution by about one and two orders of magnitude, respectively.
This component can also be successfully traced back in time, converging towards
the initial unevolved density field at z~100. We anticipate a number of
applications of our results, from predicting velocity fields to estimates of
the initial conditions of the universe, passing by improved constraints on
cosmological parameters derived from galaxy clustering via reconstruction
methods.
