The Theoretical Study On The Stability For The Three Kinds Of F(R) Modified Gravity Models

The red shift of spiral galaxies,which was discovered in 1923 by Slipher et al.,predicted the expansion of the universe,rather than the static state described by the static cosmological model,further more it was supported by Hubble's law in 1929.70 years later,the observations of type la supermovae(SNe Ia)show that this expansion was accelerated.Since then,the ac-celerated expansion of the universe has become a hot topic in the scientific community.Various theories represented by the dark energy theory and the modified theory have been proposed to explain this phenomenon,among which cosmological constant(?CDM),holographic dark energy,scalar field and so on are common candidates of dark energy model.The modified grav-ity include f(R)theory,f(R,T,Rmu nuT mu nu),and the theory of the no-local and Gauss-Bonnet gravities ect.In this thesis,the most popular modified gravity model f(R)gravity is deeply studied.First of all,the f(R)gravity is briefly introduced,and the typical f(R)model is summarized with no-coupling and coupling,respectively.Secondly,the stability of the modified theory is analyzed by energy conditions,dolgovs-kawasaki(DK)instability criteria and dynamic system stability analysis of f(R),in which the parameter of f(R)model are restricted by the energy condition and DK.Starting with Raychaudhuri equation,we review four energy conditions,and the weak energy conditions(WEC)and DK instability criteria are used to considered the model parameters and give the parameter range.In the part of dynamic stability analysis,natural units will be taken to consider the dynamic system in the case of non-minimum coupling.Then,three different f(R)gravity models with forms of trigonometric,exponential functions,and power law are considered for specific application by the above stability analysis theory,so as to obtain the properties of different model parameter ranges and critical points.Finally,dark energy models of THDE and ?HDE are selected to reconstruct with f(R))model respectively under two different scale factors.The relevant parameters are given according to appropriate initial conditions,and weak energy condition(WEC)is applied to restrict the parameters of the reconstructed model,and give the parameter ranges.