Thermodynamics Of Eddington-Born-Infeld Universe And Cosmological Evolution Under The Two-Scalar Theory

General relativity gave us a completely different understanding of gravity.At the same time,physicists began to use general relativity to explain physical problems,making up for the limitations of Newtonian gravity.However,with the continuous improvement of astronomical observation methods,physicists found that general relativity was not perfect,and there were many problems that general relativity could not explain,such as the problem of inflation in the early universe and the dark energy problem.Therefore,some schemes to modify the gravita-tional theory are put forward,which can be divided into two categories:1.modify the action;2 change the geometry used.There are many modified gravitational theories in the first category,such as scalar field theory,massive gravity,f(R)theory,f(R,T)theory,Eddington-Born-Infeld theory,etc.The second category is mainly Palatini form and affine-connection form.All these modified gravitational theories can explain to some extent the difficulties in modern astronomy and cosmologyOn the other hand,with the extensive study of black hole thermodynamics,the thermody-namic properties of the universe have attracted the attention of physicists.It has been discovered that both the first and second laws of thermodynamics can be satisfied in Einstein's universeIn this paper,we will mainly discuss two parts of work:the thermodynamics of Eddington-Born-Infeld universe and the cosmological evolution model under the two-scalar theoryFirstly,we discuss the thermodynamic properties of Eddington-Born-Infeld universe by using the traditional method in Einstein universe.By redefining Hayward's formula,we can still obtain the first law of thermodynamics and Clausius equation in the Eddington-Born-Infeld universe as same as the forms in Einstein's universe.However,the second law of thermody-namics in Eddington-Born-Infeld universe can be satisfied only under certain conditions,which is different from Einstein's universeIn addition,we generalize f(R,T)theory to two-scalar theory by imitating the relationship between f(R)theory and scalar-tensor theory,and discuss the evolution of the universe under two-scalar theory.The results show that the universe under two-scalar theory can be divided into three stages:the accelerating expansion stage,the decelerating contraction stage,and the second accelerating expansion stage.In the decelerating contraction stage,there are strong interaction and mutual transformation between the contents of the universe.Eventually universe under the two-scalar theory will evolve into a dust universe.