Theoretical Analysis On The Holographic Dark Energy Model With Generalized Entropy In The Finsler-Randers Cosmology

Since the discovery of the accelerated expansion of the universe,scientists have begun to search for the cause of the accelerated expansion of the universe.Two types of solutions have been proposed.One is introducing the exotic matter-dark energy(DE)sector characterized by negative pressure,and the other is modifying the space-time geometry of the universe,namely modifying gravity.In this thesis,several dark energy models are introduced,including cosmological constant model,holographic dark energy model and related generalized models.The common f(R)modified gravity and Finsler-Randers theory are also introduced.Finsler geometry is a natural extension of traditional Riemannian geometry,that is,Riemannian geometry is a special case of Finsler geometry.The field equations in the Finsler-Randers universe contain an additional geometric term that can be used as a dark energy fluid,so the theory is expected to provide additional insights into observing the dynamic evolution of the universe.Secondly,the Tsallis holographic dark energy model and the Rényi holographic dark energy model are studied under the Finsler-Randers cosmological theory,in which the Hubble horizon is assumed as the infrared truncation.In this setup,the density parameters,state parameters and deceleration parameters of these two kinds of generalized entropy holographic dark energy models are deduced,and the corresponding evolution images are drawn.The study shows that regardless of whether there is an interaction between dark energy and dark matter,the Two theoretical models can describe an accelerating expansion of the universe.Then,the two types of dark energy models are diagnosed by statefinder,and the images ofr-z,s-z and r-s are drawn.The differences between AC DM models and dark energy models with different interaction forms and coupling parameters can be seen,among which r-s has the best diagnostic effect.And the distance modulus of the theoretical model is compared with the observed data of supernova Ia,it is found that both cases are consistent with the observed data.Finally,the dynamic stability analysis of two kinds of generalized entropy holographic dark energy models with interaction in Finsler-Randers universe is studied.It is found that only in the Rényi holographic dark energy model,there exist dynamic attractor points,namely stable points,and in this case,The stability point is affected by model parameters and coupling parameters.