The Perturbation And Big Bounce In Rainbow Universe

Rainbow gravity as a formalism of semi-classical quantum gravity has been viewed as a generalization of Doubly Special Relativity in curved space-time. It is originally proposed by Maguejio and Smolin. The key idea in this framework is to consider the impacts due to the quantum gravity effects of particles on the background space-time. In this thesis we mainly study this formalism in following two aspects. First, we will investigate the perturbation theory of inflationary scenario in rainbow gravity formalism and derive the primordial perturbation spectrum of the scalar field. Second, we will obtain the non-singular big bounce solutions in the rainbow universe, and hopefully providing a mechanism to solve the problem of the big-bang singularity in standard cosmology.In chapter 1, we will briefly review and summarize the main ideas in rainbow gravity. First of all, Doubly Special Relativity is a kind of deformed special relativity in flat space-time, which intends to preserve the relative principle, at the same time, contains an invariant Planck length applicable for all inertial observers when the quantum gravity effects of high energy particles are taken into account. This formalism is accomplished by non-linear Lorentz transformations in momentum space. However, there is a crucial open issue in DSR, that is, the difficulty of defining the position space dual to the momentum space. As a result, people propose that maybe there does not exist a single, fixed space-time when the impact of particles on the space-time is taken into account. On the contrary, probes with different energies will detect different space-times. That is to say, the metric depends on the energy of probes, leading to a formalism of rainbow gravity. Furthermore, from rainbow metric, one may obtain an energy-dependent connection and curvature, a modified Einstein's equations. In the cosmological setting, it will give rise to the modified FRW equations.In Chapter 2 we study the inflationary scenario in rainbow gravity formalism. It is believed that there is a stage of inflation in the very early epoch of the universe. The inflationary paradigm generates density perturbations as seeds for large scale structure in the universe. In this chapter, we discuss the perturbations of inflation in the rainbow universe and derive the power spectrum. It turns out that the scale invariance of the power spectrum is preserved and the power spectrum index is unchanged. However, the magnitude of the spectrum depends on the energy of probes.In chapter 3 we obtain the big bounce solutions in rainbow cosmology. The usual Einstein's equations are modified as a one parameter family of equations in the framework of rainbow gravity. In this chapter, we derive the modified Friedmann-Robertson-Walker (FRW) equations when the cosmological evolution of radiation particles is taken into account. In particular, given some specific rainbow functions, the big bounce solutions to the modified FRW equations can be derived. Notably, to obtain a well defined rainbow metric at the moment of the big bounce, we find it seems necessary to introduce a cosmological constant which depend on the energy of probes as well, implying that a universe with a positive cosmological constant more likely undergoes a big bounce at this phenomenological level.Chapter 4 is the conclusion of the thesis.