The Non-minimally Coupled Quintessence Dark Energy Models

The observation of type la supernovae in 1998 revealed first-ly that our Universe is undergoing an accelerated expansion, which has been confirmed by various observations. This observed sce-nario can be accounted by a modification of the theory of general relativity on the cosmic scale or by the existence of an exotic en-ergy with negative pressure, dubbed as dark energy. Dark energy accounts for approximately 70% of the total energy in the present Universe. The simplest and most popular candidate of dark en-ergy is the cosmological constant. It fits almost all observational data very well, however, suffers two serious theoretical problem-s:coincidence problem and fine tuning problem,. Thus, inspired by inflation theory, some minimally coupled scalar fields, such as Quintessence, Phantom and Quintom, are proposed to explain the accelerating cosmic expansion.It is a natural generalization to consider a coupling between the scalar field and gravity(hereafter models with such couplings are referred to as non-minimally coupled models). The non-minimally coupled models can be used to explain both the infla-tion and the present accelerated expansion. In this dissertation, we mainly discuss the non-minimally coupled quintessence dark energy models. The scalar curvature is considered in two different formalisms:the metric formalism and the Palatini one.We first study the dynamical behavior and the effective e- quation of state of the non-minimally coupled models, find that the effective equation of state in Palatini formalism can cross the -1 divide line, and moreover, it oscillates around the -1 line. This oscillating behavior is a new property, which is different from the case of metric one. We also show that the Universe driven by the Palatini non-minimally coupled models will enter a dark energy dominated de-Sitter phase in the future.Then we research the linear perturbation theory of the non-minimally coupled models, analyze the evolution curves of the gravitational potential, the effective Newton constant and the linear matter growth rate, and give a comparison among the non-minimally coupled models, the minimally coupled model and the ∧ Cold Dark Matter(ACDM) model. We find that the differences between the metric and Palatini formalisms are mainly concen-trated in the low redshift region and the current observation can not distinguish them effectively.Next, we investigate the integrated Sachs-Wolfe (ISW) ef-fect and its power spectra in the non-minimally coupled models in both the metric and Palatini formalisms. We find that the ISW effect depends on the Hubble function H(a), the growth function D+(a), the dimensionless matter density Ωm(a) and the coupling function F(a). When the coupling constant of the non-minimally coupled models is negative, the differences between the metric and Palatini formalisms are negligibly small, and the ACDM model can be taken as a good approximation to the non- minimally coupled models. However, a positive non-minimal cou-pling in the Palatini formalism leads to an appreciable deviation from the ACDM model, and the differences between two different formalisms are also very obvious.Finally, we use the spherical collapse method to investigate the linear density contrast and the nonlinear overdensity parame-ter of pressureless matter in the non-minimally coupled models in the metric and Palatini formalisms. We find that all the models converge to the Einstein de Sitter(EdS) model at high redshift region, and for both formalisms, when the coupling constant is negative, the differences between non-minimally coupled models and the ACDM model are negligibly small.