http://arxiv.org/abs/1506.08649
We solve the field equations of modified gravity for $f(R)$ model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase space analysis of $f(R)$ models, both with and without the effects of radiation. Stability of these points is studied by invoking perturbations about them. We apply the conditions on the eigenvalues of the matrix obtained in the linearized first-order differential equations for stability of points. Following this, these fixed points are used for the dynamics of different phases of the universe. Certain linear and quadratic forms of $f(R)$ are determined from the geometrical and physical considerations and the dynamics of the scale factor is found for those forms. Further, we determine the Hubble parameter $H(t)$, Ricci scalar $R$ for radiation-, matter- and acceleration-dominated phases of the universe, whose time-ordering may explain an arrow of time throughout the cosmic evolution.
M. Verma and B. Yadav
Tue, 30 Jun 15
70/75
Comments: 7 pages, 6 figures
You must be logged in to post a comment.