Quantum correction to inflation and curvature perturbation

Inflation is a sudden and near exponential expansion of space in early universe. Infla- tion solved flatness problem, horizon problem and monopole problem that persisted in standard big bang cosmology. It was not only useful in solving these problem but also accounted for origin of structure in universe that we observe today. Direct observation of this phenomenon is not possible but its occurrence is confirmed by present cosmological observation. In this thesis we will investigate inflation driven by scalar field via equation of motion on classical level and with quantum corrected ones as well.First we will solve classical and quantum corrected evolution of field in different cosmological background and eventually compare results using graphs. Similarly we will explore some aspects of curvature perturbation.It is now widely ac- cepted that curvature perturbation is dominant cause of structure formation in universe. The field responsible for curvature mechanism is called curvaton. It evolves during in- flation as sub-dominant field but is independent of field driving inflation. Curvaton is subdominant during inflation so adiabatic (curvature) perturbation is first achieved by isocurvature(entropy) perturbation.After the end of inflation curvaton starts to oscillate during radiation dominated era and converts isocurvature perturbation into curvature perturbation.We will examine various potential by taking into account all the constraints and also use the fact that the model we use generates curvature perturbation of observed limit ,ζ ∼ 10−5