A HIDDEN SYMMETRY IN THE ONE-DIMENSIONAL COSMOLOGICAL MODEL

We study the non-linear evolution of the one-dimensional self-gravitat ing system in the expanding universe. In particular, we gave an explic it expression for the perturbative solutions, which reproduce the Zeld ovich exact solution properly. Then we found an infinite number of con served quantities, which indicate the existence of a hidden symmetry. Those would strongly constrain the power transfer of the density field . The above symmetry might be useful for explaining the scaling behavi or at the epoch of the singularity formation.