Aspects of Axion $F(R)$ Gravity
  We provide a compact review on recent developments on axion $F(R)$ gravity.
The axion field is a string theory originating theoretical particle that is a
perfect candidate for low-mass particle dark matter. In this review we present
how a viable inflationary phenomenology and a viable late-time evolution can be
described by an axion $F(R)$ gravity theory, in which the $F(R)$ gravity part
can drive in a geometric way the inflationary and the late-time era, and the
axion field behaves as dark matter, with its energy density $\rho_a$ behaving
as a function of the scale factor as $\rho_a\sim a^{-3}$. We also briefly
discuss the effect of a non-trivial axion Chern-Simons coupling on the
inflationary phenomenology of the $R^2$ model. Finally, we briefly discuss the
effects of a non-minimal coupling of the axion field with the curvature on
neutron stars, and also the propagation of gravity waves in Chern-Simons axion
gravity.
