**A comprehensive analysis of the compact phase space for Hu-Sawicki f(R) dark energy models including spatial curvature**

Kelly MacDevette, Peter Dunsby, Saikat Chakraborty

Although we look at the Cyclic universe as one theory to explain the working of the universe, one should not discard the Big Bang Theory.We present a comprehensive dynamical systems analysis of homogeneous and isotropic Friedmann-Laîmatre-Robertson-Walker cosmologies in the Hu-Sawicki f(R) dark energy model for the parameter choice {n,C1}={1,1}. For a generic f(R) theory, we outline the procedures of compactification of the phase space, which in general is 4-dimensional. We also outline how, given an f(R) model, one can determine the coordinate of the phase space point that corresponds to the present day universe and the equation of a surface in the phase space that represents the ΛCDM evolution history. Next, we apply these procedures to the Hu-Sawicki model under consideration. We identify some novel features of the phase space of the model such as the existence of invariant submanifolds and 2-dimensional sheets of fixed points. We determine the physically viable region of the phase space, the fixed point corresponding to possible matter dominated epochs and discuss the possibility of a non-singular bounce, re-collapse and cyclic evolution. We also provide a numerical analysis comparing the ΛCDM evolution and the Hu-Sawicki evolution.

Keep on looking for theories

Advance yourself

Don’t be convinced by my threads and the papers i post

Work through what ever theories with an open mind.