  We propose a new non-parametric method to constrain the cosmological model
through the growth factor of large-scale structure. To constrain the
cosmological model from observations such as cosmic microwave background or
large-scale structure, the power spectrum or correlation function have been
used since they are well described by the linear perturbation theory or little
correction is needed for the non-linearity; however, it is always important to
find an alternative route to constrain cosmological models in order to avoid
systematic effects due to the estimator and make the constraint more robust.Our
density fluctuation reconstruction method constrains the cosmological model
directly from time evolution of density fluctuation. We propose to apply
Kolmogorov-Smirnov test and D'Agostino's K-squared test to the distribution
function of density fluctuations, which are observed on a light cone. The
density fluctuation recovers the Gaussian distribution only if we reconstruct
the density fluctuation with correct linear growth factors. The method is
verified by the use of Gaussian random field and N-body simulations. This
method will open a new window both to separate the initial three dimensional
density fluctuation and the growth factor of large scale structure.
