In this thesis, wefirstly reviewthe dynamics of universe.Using the homogeneity, isotropy and Weyl principle, we can obtain theFriedmann - Robertson - Walker (FRW) metric. By using this metric and Einstein equation in General Relativity, one can derive two Friedmaequations. The evolution of energy density is given by these equations. Although, the standardmodel of cosmology can describe the observations of the cosmic microwave background. This model suffers from some problems such as horizon and a flatness. One way for solving these problems is the inflation model. In this model, the scale factor is exponentially grown in such a way that the Hubble radius decreases. In addition of solving these problems, the inflation model is able to explain the source ofinitial inhomogenity. After the inflationary accelerated period, and before reheating, the universe passes through a parametric resonance particle production phase known as preheating period. There are some phenomenological models which investigate the particle production during preheating. The analytic study of the preheating priod has been done by some authors. However a full Analytical study is very difficult. For numeric study, Gary Felder has developed a code with the name ``Latticeeasy” which numerically solves the nonlinear equations in this period. This code is useful for the models with scalar fields. One can easily change the ``model” file of this code to extend the code to the new models. In this thesis, we consider a model with complex scalar inflaton field coupled to the vector fields. Because of this coupling the vector fields become massive and then the conformal symmetry is brocken. In addition, in this model, the kinetic couplingis dependent on time or inflaton field. For different scalar potentials, theevolution of inflaton field and fluctuations of gauge fields are studied by numerical computing during the period of preheating. Because of some problems such as the existence of conductivity coefficients, the Latticeeasy code can not be extended to the vector field cases. For this reason, we write a code using Rung - Kutta method. Our strategy is to split fields in to a homogeneous background that depends only on cosmic time and a spatially dependent perturbation. We numerically study the evolution of fields by considering of metric perturbation. The significant quantity for our research is evolution of curvature perturbation, because by using this quantity power spectrum is given. The results show that the effects of gauge fields on curvature perturbation are completely negligible. This quantity becomes non - adiabatic for multi field cases. In our research, we show that the time evolution of curvature perturbation for gauge fields is equal to zero. Therefor the curvature is constant on the large scales. In order to study the time evolution of curvature perturbation, we have to define and calculation the non – adiabatic pressure which also was derived in this work. Keywords: Cosmology, Singularity, Entropic Force, Running Gravitational Coupling.