We present a model of dark matter based on scalar-tensor theory of gravity. With this scalar field dark matter model we study the non-linear evolution of the large-scale structures in the universe. The equations that govern the evolution of the scale factor of the universe are derived together with the appropriate Newtonian equations to follow the nonlinear evolution of the structures. Results are given in terms of the power spectrum that gives quantitative information on the large-scale structure formation. The initial conditions we have used are consistent with the so-called concordance ΛCDM model.
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