Studies On Relic Gravitational Waves, Analytical Anisotropies And Polarization Spectra Of Cosmic Microwave Background With Reionization, And Yang-Mills Dark Energy

This Thesis presents my research, under the guidance of my adviser Professor Yang Zhang, on the relic gravitational waves(RGWs), cosmic microwave background radiation(CMB) and dark energy. All of them are very active issues in modern cosmology. The observations on supernovae Ia and CMB also accelerate the studies on these subjects. They are important for understanding the basic foundation of the universe, inflation in the extreme early time and the evolution history of our cosmos. The Thesis is divided into six chapters.Chapter 1 is the short introduction of the background of cosmology, mainly about the research status and evolvement of RGWs, CMB and dark energy. The recent progress of RGWs, CMB and dark energy will be introduced here. On RGWs, we introduce the position of the gravitational waves in the research of gravitational theory and the status of their observations first. Then we mainly show the properties of RGWs and the results of our investigation. On CMB, the important meanings of the research of CMB on inflationary cosmology is first explained, then our analytical solution and main conclusion. The last of this chapter is the introduction of the dark energy problem, mainly about the origin, the observational methods, the theoretic research and the difficulties on models.The basic properties of gravitational waves are explained first in Chapter 2. And briefly introduced two kinds of important sources of gravitational waves, the periodic and pulsed sources. After that it is mainly about RGWs. The origin in the inflationary cosmology model, and the analytical evolution in the accelerating universe are shown. Then the influences of the QCD phase transition and e+e annihilation effect are considered. These two progresses are able to decrease the amplitude of RGWs obviously. At the end of this chapter, we introduce a simple method to calculate the spectra of RGWs with the primordial spectrum, the transfer function method, which can derive the RGWs spectra with the influence of free neutrinos.In Chapter 3 we study the generation of the CMB temperature anisotropies and polarization, whose evolutional equation are written down explicitly. The emphases of our discussion is mainly on the case of the tensorial perturbations (RGWs) as the source. We use half Gaussian functions to fit the visibility function of the decoupling process to improve accuracy of the fitting formula. Then the time integration for the polarization mode including the decoupling process can be analytically carried out approximately, resulting in its analytical expression, which contains explicitly the RGWs, the decoupling time, the decoupling width, and the damping factor. Integrating over the wavenumber, we arrive at the expressions of power spectra of temperature anisotropic and polarization, C_l^EE, C_l^BB, C_l^TT and C_l^TE, among which, the the temperature perturbation C_l^TT and the temperature-polarization cross power spectra C_l^TE are derived here for first time. These demonstrate explicitly the impact of the physical processes and the cos-mological parameters upon the power spectra. For the technique treatment, we improve the decaying factor coming from the Fourier transformation of visibility function. The analytical results are compared with the numerical ones, and they are very similar to each other on the range l < 600 of large angular scales, and the error is smaller than 20%. Two kinds of RGWs sources are used here, one with neutrino free-streaming effect and another without it. It is found that the neutrino free-streaming has the effect of damping the amplitudes and shifting the position of the peaks of CMB spectra. With the help of these analytical expression, the influence of the cosmological parameters are also analyzed, such as the baryon fraction and the power index of primordial perturbations generated during the inflation.Chapter 4 mainly discuss the influence of reionization on CMB spectra. Different from the known decoupling epoch, the reionization process is less known as a physical process, either observationally or theoretically. We examine three reionization models with different ionized fractions. With this we calculate the respective differential optical depth, the integral optical depth, and the visibility function. Similar to the treatment for the decoupling epoch, the half Gaussian approximation to the visibility function is also applied here in the time integration. Then the analytical expressions of mode functions of temperature anisotropies and polarization of CMB are derived. Each mode function is compose by two parts, contributed by the decoupling and the reionization, respectively. The analytical expressions of reionized CMB spectra are derived for the first time. Compared with the numerical solution, in the range of l G (30, 600) our analytical results are still quite accurate, and in the range l < 20 for the reionization bump the error is 15%. Through the comparison of three reionization models it is shown that the reionization optical depth is the most important parameter, which determines the relative amplitudes of the reionization bumps and of the primary peaks of CEEl and CBBl. The effect of reionization on CTTl and CTEl is to increase the amplitudes on very large scales. It is significant that the explicit dependence of the amplitude of bumps and primary peaks upon the reionization are first analytically derived. These will greatly facilitate the study of the degeneracies, between the reionization optical depth and the amplitude of primordial perturbations, the reionization optical depth and primordial power spectrum index. The results will useful in analysis of the future observational data to break these degeneracies.In Chapter 5 the observational evidence of dark energy is mentioned. We review briefly several popular dark energy models and introduce the fine tuning problems and coincidence problem that facing all the dark energy models. Then we focus on the quantum Yang-Mills condensate (YMC) dark energy model, explain its theoretical foundation, and present the model in the quantum 1-loop, 2-loop and 3-loop cases. The dynamical equations of the YMC dark energy model, both coupling and non-coupling with the matter and radiation components, are fully analyzed and solved in great details. The calculations show that, at the radiation-matter equality, for the initial density of YMC in a whole range of stretching over 18 orders of magnitude, the dynamic evolution always results in the same cosmic status of the present universe:ΩΛ- 0.7,Ωm 0.3. The stability analysis tells that the dynamic evolution of this model is not influenced by small perturbations. It is a stable attractor solution. So, in the sense of modeling, one can say that YMC model solve the coincidence problem naturally. We also find that the equation of state w of YMC approaches -1 during the evolution. If the coupling with the matter component is included, w can cross over -1 easily. We also find that the above dynamical evolution actually holds for the 1-loop, 2-loop and 3-loop YMC models. That is, this dark energy model is stable with the increase of the number of the loops of quantum corrections. In comparison, the conventional scalar dark energy models have difficulty in achieving all these desired properties simultaneously. Finally we compare our model with observational parameter.The summary and future outlook are presented in the last Chapter.