Abstract:
In this work, we studied the phase space of f(R) gravity in the presence of a misalignment
axion, including parity violating Chern–Simons terms. We construct the autonomous dynamical
system by using appropriate dimensionless variables and find the cosmological attractors of the
phase space, which are basically the fixed points of the autonomous dynamical system. We focus
on the R
2 model and the misalignment axion potential near the minimum. We demonstrate that the
Chern–Simons terms have no effect on the phase space. We found four distinct, possibly unstable
fixed points with physical significance. Specifically, we found two identical de Sitter fixed points, one
radiation domination fixed point, and one dark matter dominated fixed point. Thus, in the presence
of a kinetic misalignment axion, the vacuum f(R) gravity contains all of the cosmological fixed points
that can characterize all of the known evolution eras of our universe.
