Cosmology is the study of the universe as a whole. It deals with the origin and evolution of the universe. Our current understanding of our universe is based on the application of theory of general relativity to the universe. The standard theory of cosmology is able to explain many of the observational facts about the universe with great success, such as the expansion of the universe, primordial nucleosynthesis, origin and spectrum of Cosmic Microwave Background Radiation(CMBR) etc. Despite of its great success, it remains silent about some of the most profound questions related to the initial conditions of our universe. There are problems such as the horizon problem and the flatness problem for which the standard theory of cosmology offers no solution. The solution to these problems is provided by the theory of inflation. In addition to solving the above problems, Inflation, as a bonus, provides seed for structure formation in the universe. The theory of Inflation was proposed to solve the problems associated with the standard (FRW) cosmology. Inflation postulates the existence of a field φ, the inflaton, associated with which was the potential V (φ). The field was slowly rolling for some duration from its local minima to global minima. During this small duration of slow roll, φ was the dominant form of energy. The space experienced a period of exponential expansion. We have learned a great deal about inflation, but, we don’t know much about the potential V (φ) itself. There exist hundreds of models of inflaton, with different V (φ)s. The predictions of any successful model should match with the observational/experimental values of the parameters involved. Here we study few such models to find out if they can be the potential inflaton. Also we explore the basic ideas about structure formation due to the quantum fluctuations in inflaton.
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