Inflation theory is the most successful model to solve the problems of the standard model of cosmology. In this thesis, first we study the dynamic of the simplest form of the inflation model which contains scalar field called inflaton. Inflationary cosmology is a framework for generating the initial fluctuations which are the origin of anisotropies of cosmic microwave background (CMB). The Inflationary theory predicts the power spectrum of initial perturbations. In this project, first we obtain the power spectrum for the scalar and tensor perturbations. Then by adding a term to the perturbation equations, we calculate the new power spectrum. Here, we use the CAMB code to generate the CMB angular power spectrum. We then modify the standard power spectrum of CAMB and rederive the new angular power spectrum. We also compare it with the CMB data that shows the new power spectrum has a better fit with data for ? ? 50 . In this region the new model predicts a power defieciency which is consistent with recent CMB data.
