On The Theoretical Study Of The Related Problems To The Polytropic Gas Dark Energy Model

Ia supernova observations in 1998 showed that our universe is speeding up.It is believed that dark energy as a power source for the accelerated expansion of the universe.In recent years,physicists have proposed many dark energy models to explain the accelerating expansion of the universe.The simplest model is the cosmological constant model.The value of the state param-eters of the model is-1,which is in good agreement with the observed results.However,there are still many problems,such as coincidence problem and fine tuning problem.In order to solve these problems,some dynamic dark energy models have been proposed one after another.The state parameters of these dark energy models evolve with time.Among these models,the most common models are quintessence model,phantom model and holographic dark energy model etc.In addition to explaining the phenomenon of cosmic acceleration expansion,these models also have their own shortcomings,such as the state parameters of the quintessence model cannot cross through-1,the phantom model predicts that the universe will Big Rip in the future,and so on.The polytropic gas model is introduced in this paper.It is a phenomenological model,in which the Chaplygin gas(CG)model and the Generalized Chaplygin gas(GCG)model can be included as a special case.lt can explain the phenomenon of cosmic acceleration expansion at present.In this thesis,the basic principles of cosmology and several common dark energy models are introduced,and then the polytropic gas model is mainly studied.Under the background of the flat universe,the dynamic evolution of the polytropic gas model under the condition of no interaction and four different interactions between dark energy and dark matter is discussed in depth.The evolution at trends of state parameters,deceleration parameters and density pa-rameters with redshift z are plotted,compared with astronomical observations.It is found that the evolution of cosmological quantity in the presence of interaction is in good agreement with astronomical observation data,and it is concluded that there will be no Big Rip of the universe in the future.After that,statefinder diagnosis and Om diagnosis are discussed for the model.The two kinds of geometric diagnosis can distinguish the dark energy model in various cases.Through the analysis of the autonomous system and its stable point,the stability of the poly trop-ic gas model is discussed,and the interaction parameters are restricted.Through the analysis,it is found that the dynamiced system of the polytropic gas model with interaction has attractors when the appropriate value of the interaction parameter is taken.At the end of the paper,the thermodynamic properties of the polytropic gas model are studied,and the relationship between the interaction and the thermodynamic fluctuations is obtained.