ﻻ يوجد ملخص باللغة العربية
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the `attractor solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve the accuracy and range of the approximation by means of Pade approximants and compare with the slow-roll approximation.
We apply a new global dynamical systems formulation to flat Robertson-Walker cosmologies with a massless and massive Yang-Mills field and a perfect-fluid with linear equation of state as the matter sources. This allows us to give proofs concerning th
We compute cosmological perturbations for a generic self-gravitating media described by four derivatively- coupled scalar fields. Depending on the internal symmetries of the action for the scalar fields, one can describe perfect fluids, superfluids,
We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lema^itre-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of scalar field
The warm dark matter (WDM) can be described by simple and useful model called reduced relativistic gas (RRG). In this work, it is analytically constructed the scalar field actions minimally and non-minimally coupled to gravity, which are equivalent t
We prove here a long standing conjecture in general relativity, that if barotropic perfect fluid is moving in a shear free way, then it must be either expansion free or rotation free.