Frame-invariant approach to higher-dimensional scalar-tensor gravity

TL;DR

This paper develops a frame-invariant formulation of higher-dimensional scalar-tensor gravity theories, including 5D braneworld models with multiple scalar fields, to facilitate consistent analysis across different frames and dimensions.

Contribution

It generalizes the construction of frame-invariant quantities to D-dimensional scalar-tensor theories and applies this to 5D braneworld scenarios with multiple scalar fields.

Findings

Constructed frame-invariant quantities for D-dimensional scalar-tensor theories.

Extended the invariant formulation to 5D braneworld models.

Analyzed thick brane solutions with multiple scalar fields.

Abstract

The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these theories in terms of quantities that are invariant under frame transformations. Furthermore, in view of the description of gravity and its geometry motivated by string theory, such a formulation could be extended to include theories of extra spatial dimensions. In the present article, we generalize the construction of frame-invariant quantities, concerning a general, $D$-dimensional scalar-tensor theory. Then, we limit our scope to the 5D braneworld scenario, where we study thick brane solutions that are localized on the 3-brane and extend the invariant formulation to the case of multiple scalar fields (non-)minimally coupled to gravity.