Study On Very Early Universe

The Bing bang cosmology plays a very important role in the modern physics. It can make some successful predictions of our universe and have been confirmed by the later experiments. However, there are still many questions that big bang model can not give the reasonable answers. By introducing the inflationary scenario, some of these problems for instance, horizon problem, flatness problem as well as magnetic monopole problem can be completely or partly resolved. Different from these problems, in order to resolve the singularity problem, dark energy problem and the origin of large scale structure, we have to resort to the quantum gravity theory.In this thesis, firstly, we give a review on the standard cosmology and the inflationary model. Then we focus on the singularity problem and some possible ways to resolve such problem in semi-classical quantum cosmologies.Secondly, we introduce a special modified dispersion relation, and investigate its influence on the background dynamics. Thanks to the thermal description of gravity on the causal horizon, we obtain a modified Friedmann equation which contains a bounce solution. Then we discuss the possibility of the initial bounce. In the extremely high energy region which is close to Planck energy, the big bounce happens indeed. Thus, in our picture, the singularity problem is resolved in some ways.Thirdly, we review on some fundementals of thermal fluctuations in the very early universe, which mainly contains calculation of the power spectrum and non-Gaussianity. And we also give a brief introduction to three popular semi-classical cosmological models which are introduced to overcome the no go theorem in the standard model. Then we investigate the thermal fluctuations in a viscous universe. We find that due to the effect of viscosity, modes of thermal fluctuations have a very different behavor comparing with the ideal fluid case after corssing the horizon. Thus, the no go theorem of gaining scale-invariance is broken. When w≈α-1 or w≈-1/3 with a non-vanishing viscous coefficient, the power spectrum is a scale invariant one. Moreover, we calculate non-Gaussianity in this model. we find the non-Gaussianity is suppressed in the de Sitter expansion case w≈α-1, while it is observable as well as scale invariant when the phantom like condition w≈-1/3 withα≈4/3 is satisfied.