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

TL;DR

This paper explores a ghost-free scalar-tensor theory in the Palatini formalism, demonstrating its desingularization capabilities, duality with Einstein gravity, and exact solutions including cosmological models, geons, and pp-waves.

Contribution

It introduces a novel scalar-tensor theory free from ghosts, establishes its duality with Einstein gravity, and constructs exact solutions illustrating desingularization and wave propagation.

Findings

Theory is free from Ostrogradsky ghosts.

Disformal duality with Einstein gravity under specific conditions.

Exact solutions include non-singular cosmology, geons, and pp-waves.

Abstract

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. We also construct the exact pp-waves of this theory propagating at the speed of light.