Generalisation of Conformal-Disformal Transformations of the Metric in Scalar-Tensor Theories

TL;DR

This paper explores new classes of invertible conformal and disformal metric transformations involving higher derivatives in scalar-tensor theories, and applies them to develop extended mimetic gravity models with potential cosmological implications.

Contribution

It introduces novel invertible higher-derivative conformal and disformal transformations and uses them to construct extended mimetic gravity theories.

Findings

Constructed new invertible conformal transformations with higher derivatives.

Developed extended mimetic gravity models using these transformations.

Analyzed cosmological properties of the new theories.

Abstract

We study new classes of metric transformations in the context of scalar-tensor theories, which involve both higher derivatives of the scalar field and derivatives of the metric itself. In general, such transformations are not invertible as they involve derivatives of the metric, which typically leads to instability due to Ostrogradsky ghosts. We show, however, that a certain class of this type of transformations is invertible: we construct new examples of invertible conformal (and also disformal) transformations with higher derivatives. Finally, we make use of these new transformations to construct extended mimetic theories of gravity, and we study their properties in the context of cosmology.