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We propose a new non-parametric method to constrain the cosmological modelthrough the growth factor of large-scale structure. To constrain thecosmological model from observations such as cosmic microwave background orlarge-scale structure, the power spectrum or correlation function have beenused since they are well described by the linear perturbation theory or littlecorrection is needed for the non-linearity; however, it is always important tofind an alternative route to constrain cosmological models in order to avoidsystematic effects due to the estimator and make the constraint more robust.Ourdensity fluctuation reconstruction method constrains the cosmological modeldirectly from time evolution of density fluctuation. We propose to applyKolmogorov-Smirnov test and D'Agostino's K-squared test to the distributionfunction of density fluctuations, which are observed on a light cone. Thedensity fluctuation recovers the Gaussian distribution only if we reconstructthe density fluctuation with correct linear growth factors. The method isverified by the use of Gaussian random field and N-body simulations. Thismethod will open a new window both to separate the initial three dimensionaldensity fluctuation and the growth factor of large scale structure.

Density Fluctuation Reconstruction using KS test and D'Agostino's K-squared test