Properties of the exact analytic solution of the growth factor and its applications
Abstract
There have been the approximate analytic solution Silveria and several approximate analytic forms 0508156,Carroll,0303112 of the growth factor Dg for the general dark energy models with the constant values of its equation of state after Heath found the exact integral form of the solution of Dg for the Universe including the cosmological constant or the curvature term. Recently, we obtained the exact analytic solutions of the growth factor for both = -1 or -13 SK1 and the general dark energy models with the constant equation of state SK3 independently. We compare the exact analytic solution of Dg with the other well known approximate solutions. We also prove that the analytic solutions for = -1 or -13 in Ref. SK1 are the specific solutions of the exact solutions of the growth factor for general models in Ref. SK3 even though they look quite different. We scrutinize the issue of using the well known parameterizations of the growth index and its parameter given in Ref. WS to obtain the growth factor for general dark energy models. We also investigate the possible extensions of the exact solution of Dg to the time-varying for the comparison with observations.