Abstract
We investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. We assume p=(gamma -1)mu -dfrac{A}{mu ^alpha } as equation of state where mu is the matter-energy density, p is the pressure, alpha is a parameter which can take on values 0<alpha le 1 as well as A and gamma are positive constants. We draw the state spaces and analyze the nature of the singularity at the beginning, as well as the fate of the universe in the far future. In particular, we address the question whether there is a solution which is stable for all the cases.
Highlights
We investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods
The only thing to do is to use either perturbation or numerical solution methods. There is another method that allows some critical properties to be determined about the solutions without knowing the exact solution of the system of equations. In such an approach to a system of differential equations; a dynamical system is introduced by making the variables dimensionless as well as redefining the differentiation variable to cover all of the IR, and dynamical system theory (DST), which is introduced by Poincare at the end of the nineteenth century, is a pplied[1,2,3]
If contraction starts with enough( + A)and positive curvature, universe evolve to an expanding
Summary
We investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. There is another method that allows some critical properties to be determined about the solutions without knowing the exact solution of the system of equations In such an approach to a system of differential equations; a dynamical system is introduced by making the variables dimensionless as well as redefining the differentiation variable to cover all of the IR, and dynamical system theory (DST), which is introduced by Poincare at the end of the nineteenth century, is a pplied[1,2,3]. Even though it is possible to reduce the number of equations or variables by assuming properties about spacetime such that spherical symmetry, homogeneity and isotropy, it is still not easy to find a solution This is the case in the field of cosmology. The description of the following two universes is of great importance for the evolution of the universe: the nature of the singularity at the beginning, and the fate of the universe in the far future
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