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

TL;DR

This paper develops reconstruction methods for modified gravity theories, including $f(R)$ and Yang-Mills/Maxwell, to model cosmic acceleration, comparing different schemes and exploring physical equivalence of frames.

Contribution

It introduces and compares two reconstruction schemes for $f(R)$ and Yang-Mills/Maxwell theories, highlighting their differences and implications for cosmological modeling.

Findings

Reconstruction schemes can model transient phantom behavior without matter.

Comparison reveals potential physical non-equivalence of different frames.

Explicit examples demonstrate the application of methods to Yang-Mills/Maxwell theories.

Abstract

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.