Theoretical And Numerical Studies Of Interacting Dark Energy Models

Dark energy and dark matter are two major scientific issues in fundamental physics in the 21st century.Both are indirectly detected via their gravitational effects,obser-vationally,which provides us more room to study the possible interaction between dark energy and dark matter.In theory,such a dark sector interaction can help alleviate several theoretical problems of dark energy,such as the cosmic coincidence problem,and also induce new features to structure formation However,there exists a large-scale insta-bility in models of dark energy interacting with dark matter,generally called interacting dark energy models(IDE),which behaves as the blow up of the urvature perturbation on the large scales for some specific values of the dark energy equation of state w and the coupling constant β.The large-scale instability seriously hinders the studies of IDE.Until this problem is solved,we have to investigate IDE models in part of their parameter space.In practice,the relatively stable models with Q(?)ρde on the condition of ω>-1 and β>0 are more favored by cosmologists.Nevertheless,such models also suffer from an unphysical result that the density of dark matter ρc will become negative in the future.In this thesis,we devote to solving the large-scale instability of IDE,and perform the observational constraints on the IDE models after solving this issue.We also give discussions on the modified gravity theory and sterile neutrio cosmology,which is a valuable supplement to this thesis.We realized that both the large-scale instability of IDE and the instability when ωcrosses the phantom divide w=-1 in a dynamical dark energy model,are related to the calculation of the pressure perturbation of dark energy.Inspired by the common solution of the phantom-divide instability,we proposed to use the Parametrized Post-Friedmann(PPF)to handle the cosmological perturbations of IDE.Unlike the standard linear perturbation theory,the PPF approach completes the dark energy perturbation system by establishing the relationship between the momentum density of dark energy and that of other components on the large scales,rather than directly handling the pressure perturbation of dark energy.We proved that the PPF framework of IDE can successfully solve the large-scale instability issue in the whole parameter space.Before we successfully establish the PPF approach for IDE models,we studied a specific IDE model obtained from a decomposed generalized Chaplygin gas model.Such IDE model can not only keep the perturbation stable when w>-1 and β>0,but also solve the future unphysical ρc problem.With current observations,we obtained its parameter space at ω>-1 and β>0,finding that the condition of β>0 is supported by observations.With the PPF approach of IDE available,we for the first time have the power to probe the full parameter space of IDE models.We constrained the Q= 3βHpc model with current observations,and we handled its perturbation with the PPF approach.Then for the first time,we obtained its correct and full constraint results.We further constrained the widely studied Q = 3βHρde model with the help of PPF approach.For the possible degeneracy between coupling constant and other parameters,we employed the information of growth rate from the redshift-space distortions(RSD),and we found that RSD data play a crucial role on reducing the error of β.Comparing our results with those of the previous works,we found that the previous constraint resultsobtained by assuming w>-1 and β>0 can not reflect the true preference of the observational data.We also investigated the interacting vacuum energy models which is a one-parameter extension of the standard ACDM model,testing the possible departure of the ACDM model in view of the interaction between dark energy and dark matter.Using different observational data combination to constrain two specific interacting vacuum energy models,we concluded that the ACDM model still fit the data well at 2a level.Besides,we measured the growth index in a universe with sterile neutrinos,finding that a light sterile neutrino can reconcile the tension between the large-scale surveys and the ∧CDM model,making the constraint results of growth index more close to the expected value of general relativity.We also tried to simultaneously constrain the f(R)model and the mass of sterile neutrinos with the measurements of the scale-dependent growth rate.We obtained a tight constraint for the f(R)parameter,and found that there exist a slight degeneracy between the f(R)parameter and the sterile neutrino parameters.