Ghost-free Palatini derivative scalar-tensor theory: desingularization and the speed test

Understand

We disclose remarkable features of the scalar-tensor theory with the derivative coupling of the scalar field to the curvature in the Palatini formalism.

• Using the disformal transformations, we show that this theory is free from Otrogradski ghosts.
• For a special relation between two coupling constants, it is disformally dual to the Einstein gravity minimally coupled to the scalar, which opens the way to constructing several exact solutions.
• The disformal transformation degenerates at the boundary of the physical region, near which the properties of desingularization are revealed, illustrated by exact solutions: non-singular accelerating cosmology and a static spherically symmetric geon.