abstrac The Friedmann-Robertson-Walker (FRW) metric is given using the homogeneity and isotropy principles. For this metric and for a perfect fluid, the Einstein equationsare solved and result in the Friedmann equations. The standard model of cosmology encounters with horizon and flatness. The inflation model is a solution for such problems. During inflationHubble radius is reducedand this make to justify the problems of standard cosmology. In inflationary models the slow roll condition is necessary for inflating the space time. This condition is given by a flat potential. Moreover, the quantum fluctuations of inflaton fieldcan explain the large-scale structures. The basic parameter in large scale study is the curvature perturbation. It has been formulated a large dir=rtl Keywords: Standard cosmological model, Inflation model, Power spectrum, Spectral index, Commoving curvature perturbation,Power-law inflation model, Graceful exit.
