Interacting Phantom Dark Energy And The Linear Perturbation Of Matter Density

Type 1a supernova data reveal that our universe is under-going an accelerating expansion in 1998, and this discovery is confirmed by the other observational data of astronomical tests, such as the tests of the latest type la supernova data, cosmic mi-crowave background radiation, and large scale structure. Dark energy, which is required to have sufficient negative pressure, is proposed to explain this mysterious phenomenon. The main dark energy models include the cosmological constant (ACDM) and the scalar field such as Quintessence. Phantom and Quintom. ACDM model is the simplest candidate of dark energy and fits the data of astronomical tests very well. However it suffers from two serious theoretical problems:the problem of fine-tuning and the coinci-dence. The recent SNe data seem to favor the dark energy with the present equation of stateω< - 1, and so Phantom model is highly valued by the cosmologist. Phantom field has a negative kinetic term in its Lagrangian, which may result in some new fea-tures, such as the future singularity of big rip. Recently, the loop quantum cosmology has been studied extensively and researches show that there is no big bang singularity in the loop quantum cosmology due to the effects of loop quantum. In chapterⅢof this dissertation, we study the dynamics of a phantom scalar field dark energy interacting with dark matter in loop quantum cosmology. Two kinds of coupling of the formαpmφ(caseⅠ)and 3βH(ρφ+ρm) (caseⅡ) between the phantom energy and dark matter are examined with the potential for the phantom field taken to be exponential. For both kinds of interactions, we find that the future singularity appearing in the standard Friedmann-Robertson-Walker cosmology can be avoided by loop quantum gravity effects. In caseⅡ, if the phantom field is initially rolling down the potential, the loop quantum effect has no influence on the cosmic late time evolution and the universe will accelerate forever with a constant energy ratio between the dark energy and dark matter.Modified gravity theories, in which the theory of general rel-ative gravity is modified in the cosmic scale, constitutes an inter-esting alternative to dark energy cosmology. The main modified gravity models include Dvali-Gabadadze-Porrati (DGP) brane-world model and f(R) model. Studies show that modified gravity model and dark energy model can produce the same history of universe expansion, so one of the most important tasks is how to discriminate them. Recently, it is argued that the measure-ment of growth functionδ(z)=δρm/ρm might be competent in this regard. If two models, especially dark energy and modified gravity models, share the same cosmic expansion history, they might have a different growth history. Thus, they could be dis-tinguished from each other. In chapter IV, we study the growth of matter linear perturbation in DGP model with the growth indexγas a function of redshift z. At the linear approxima-tion:γ(z)≈γ0+γ10z, we find that, for 0.2<≤Ωm,0≤0.35,γ0 takes the value from 0.658 to 0.671, andγ10 ranges from 0.035 to 0.042. With three low redshift observational data of the growth factor, we obtain the observational constraints onγ0 andγ10 for the ACDM, DGP and a viable f(R) model-Starobinsky model, and find that the observations favor the ACDM model, but at the 1σconfidence level, ACDM and DGP are consistent with the observations, but f(R) model is consistent with the observations only at the 2αconfidence level. Then we propose a parametriza-tion,γ(z)=γ0+(?)γ10 for growth index of the matter linear perturbation and find thatΩmγapproximates the growth factor f very well both at low and high redshfits for both kinds of models. Therefore, our parametrization may be robustly used to constrain the growth index of different models with the observational data which include points for redshifts ranging from 0.15 to 3.8, thus providing discriminative signatures for different models. Using this parametrization, we discuss the observational constrains on theωCDM model, DGP model and Starobinsky model with all current growth factor data, and we find that theωCDM model is consistent with the observational data at the 1σconfidence level, while the DGP model or Starobinsky model is only consistent with observations at 2σconfidence level.