The relative density parameter ? DM of dark matter can be calculated based on the ratio of dark matter interactions with other particles using standard model of cosmology and Boltzmann equation. The interaction rate is a function of the scattering cross section. Therefore, scattering cross section and decay rate can be calculated in order to obtain ? DM .The parameter space of different models of dark matter can be obtained by applying the experimental constraint on ? DM . In this thesis we investigate the real scalar model for dark matter with Z 2 symmetry (keeping terms up to order ? 4 ). By considering the abundance of dark matter data, using Planck satellite, we are led to determine a constraint on the space parameters of this model.
