Theoretical Study On Cosmological Evolution And Related Problems Of Sharma-Mittal Holographic Dark Energy Model With Viscosity

A series of astronomical observational data show that the universe is in a stage of acceler-ating expansion at present.Various dark energy models with negative pressure are proposed to explain this phenomenon,such as Quintessence,K-essence,Chaplygin gas,holographic dark energy and so on.In this thesis,cosmological evolution and geometric diagnosis of Sharma-Mittal holographic dark energy(SMHDE)model with viscosity are studied.In a flat FRW universe,the effects of the model parameters on the evolutionary trajectory of density parameters,state parameters and deceleration parameters in the SMHDE model are firstly discussed in this thesis,and the optimal values of them are given on the basis of analysis.Then,we study the evolutionary laws of the cosmological quantities of this model when there is no interaction between dark energy and dark matter and there are four different interactions.The evolutionary curve shows that the universe will gradually become dominated by dark en-ergy.Furthermore,in order to distinguish the model from ACDM model,we also perform Statefinder geometric diagnosis,Statefinder hierarchy geometric diagnosis and Om geometric diagnosis.The results show that all the three geometric diagnoses can distinguish this model from the ACDM.Secondly,we discuss the cosmological evolution and geometric diagno-sis of this model when only dark energy with viscosity and only dark matter with viscosity,respectively.It is found that when only dark energy has viscosity,the viscosity has no effect on density parameter and deceleration parameter.But the evolutions of various cosmological quantities will be significantly affected by the viscous property in the case of dark matter with viscosity.We also carry out the Statefinder geometry diagnosis and Om geometry diagnosis for the interacting SMHDE model with viscosity.From their respective evolutionary images,we can see that these two diagnostic methods can not only distinguish the difference from ACDM model,but also can directly reflect the obvious influence of viscosity coefficient and coupling parameters on the dark energy model.Finally,the thermodynamic properties of the model are discussed,and the second law of thermodynamics and the modified expression of entropy of the model are derived.From the evolutionary track of entropy change rate,it can be seen that the interaction model with viscosity conforms to the second law of thermodynamics during the evolution.