Study Of Properties Of Dark Energy Models Under The Framework Of General Relativity

In the early 1990's,people were very sure about about the expansion of the Universe.The Universe may have enough energy density to stop its expansion and recollapse,or it might also have so little energy density that it would never stop expanding,however,the gravity was certain to slow the expansion as time went on.Granted,it hasn't been observed that the expansion is slowing,but,theoretically,the Universe had to slow,Because the universe is full of matter that would be pulled together due to the attraction force.Then came 1998 and the Hubble Space Telescope observations of very distant supernovae that showed that,a very long time ago,the Universe was expanding more slowly than it is today.So,in fact,the expanding of the Universe was not becoming more and more slow,on the contrast,it has been accelerating.Nobody was expecting this result.But there must be something was causing it.Then theorists put out three sorts of ways to explain it.Maybe it was a result of Einstein's theory of gravity should containe what was called a cosmological constant.Maybe there was some strange kind of energy-fluid that filled space.Maybe there is something wrong with Einstein's theory of gravity and a new theory could include some kind of field that creates this cosmic acceleration.Theorists still don't know what the correct explanation is,but they have given the solution a name.It is called dark energy.In this paper,we mainly introduce some dark energy models in the context of general relativity,including single scalar field dark energy model and coupled dark energy models.We analyzed the properties of ”catalyst” type of interaction between dark energy and dark matter by using dynamical system analysis.First of all,we begin with a brief introduction to dynamical systems,fixed points,linear stability theory.In this paper,we use this technique to study the cosmological models,focusing on the late-time behavior of our Universe,in particular on its accelerated expansion.Secondly,we focus on standard model and the cosmological constant problem coincidence problem caused by this model.We also present a large number of dark energy models that try to solve these problems,ranging from canonical and non-canonical scalar fields,mainly including quintessence,phantom,quantom and k-essence dark energy models.What's more,we study coupled dark energy models,including coupled perfect fluids model,coupled quintessence model and coupled non-canonical scalar field model,then we especially focus on three specific interactions of dark sector in the existence of baryonic matter and radiation.We attempt to assume baryonic matter and radiation can affect the conversion between dark energy and dark matter like the way catalyst influences the conversion rate of two materials in some reversible chemical reactions.Then we present phase space analysis for every special interaction model.For every case,we obtain a stable attractor solution that can alleviate the coincidence problem.Finally,we made a conclusion and outlook in the end of our paper.We reviewed our results and deficiencies of our works,and made a outlook of future direction.