A Study Of Renomalizable Inflationary Cosmological Model And The Related Problems

In this thesis, we briefly review the standard cosmology model, which is built on the assumption that our universe is homogeneous and isotropic. From this assumption,we could get Robertson-Walker Metric and get equation of motion through combining Einstain equation. At the same time, we introduce several problems caused by standard cosmology model including horizon problem, flatness problem and magnetic monopole problem and bring the inflationary cosmology model to our sight to deal with these problems. We also systematically study the renormalizable three-term polynomial inflation in the supersymmetric and non-supersymmetric models. The supersymmetric inflaton potentials can be realized in supergravity theory, and only have two independent parameters. We show that the general renormalizable supergravity model is equivalent to one kind of our supersymmetric models. We find that the spectral index and tensor-to-scalar ratio can be consistent with the Planck and BICEP2 results, but the running of spectral index is always out of the 2 range. If we do not consider the BICEP2 experiment, these inflationary models can be highly consistent with the Planck observations and saturate its upper bound on the tensor-to-scalar ratio(≤0.11). Thus, our models can be tested at the future Planck data analysis and QUBIC experiments. We also consider the polynomial inflation with large tensor-to-scalar ratio which can be consistent with the Quantum Gravity(QG) corrections and Effective Field Theory(EFT). For the slow-roll inflation,we obtain the small field inflation with large , due to the decreasing , which becomes fast increasing near the end of slow-roll. So the Lyth bound is violated obviously. Interestingly, we find an excellent practical bound on the inflaton excursion in the format + √, where is a small real number and is at the order 1. In addition, even for = 0.11 and = 55, we show that /Plcan be at the order of 0.1, and thus such polynomial inflation is indeed consistent with the QG corrections and EFT.