| Sumario: | We provide a compact review on recent developments on axion F(R) gravity. The axion field is a string-theory-originated 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 ρ behaving as a function of the scale factor as ρ ∼ a. We also briefly discuss the effect of a non-trivial axion Chern-Simons coupling on the inflationary phenomenology of the R 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.
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