Reconstructing cosmic acceleration from modified and non-minimal gravity: The Yang-Mills case

A variant of the accelerating cosmology reconstruction program is developed for $f(R)$ gravity and for a modified Yang-Mills/Maxwell theory. Reconstruction schemes in terms of e-foldings and by using an auxiliary scalar field are developed and carefully compared, for the case of $f(R)$ gravity. An example of a model with a transient phantom behavior without real matter is explicitly discussed in both schemes. Further, the two reconstruction schemes are applied to the more physically interesting case of a Yang-Mills/Maxwell theory, again with explicit examples. Detailed comparison of the two schemes of reconstruction is presented also for this theory. It seems to support, as well, physical non-equivalence of the two frames.