Cosmological dynamics in f(R) gravity
  In this paper, we study the cosmological viability conditions, the
phase-space dynamics, and the cosmological evolution of f(R) gravity. In
contrast to most previous works in the literature, which analyzed the
background dynamics of f(R) gravity by means of a dynamical system, we proceed
by focusing on the equivalent scalar field description of the theory, which we
believe is a more intuitive way of treating the problem. In order to study how
the physical solutions evolve in f(R) cosmology, we explore the cosmological
dynamics of a range of f(R) models, including models that yield a large
hierarchy of scales and are singularity free. We present generic features of
the phase-space dynamics in f(R) cosmology. We study the global structure of
the phase space in f(R) gravity by compactifying the infinite phase space into
a finite space via the Poincare transformation. On the expansion branch of the
phase space, the constraint surface has a repeller and a de Sitter attractor;
while on the contraction branch, the constraint surface has an attractor and a
de Sitter repeller. Generally, the phase currents originate from the repeller
and terminate at the corresponding attractor in each space. The trajectories
between the repeller and the attractor in the presence of matter density are
different from those in the vacuum case. The phase analysis techniques
developed in this paper are very general, and can be applied to other similar
dynamical systems.
