Late time cosmic acceleration in modified S\'{a}ez-Ballester theory

TL;DR

This paper extends the Se1ez-Ballester scalar-tensor theory to higher dimensions, deriving dark energy geometrically and offering insights into lower gravity theories without adding matter by hand.

Contribution

It introduces a new extended geometric framework of the Se1ez-Ballester theory with two scalar fields, linking dark energy to pure geometry in higher dimensions.

Findings

Dark energy can be derived from geometry in this framework.

The theory naturally incorporates extra dimensions.

Provides a geometric perspective on lower gravity theories.

Abstract

We establish an extended version of the modified S\'{a}ez-Ballester (SB) scalar-tensor theory in arbitrary dimensions whose energy momentum tensor as well as potential are pure geometrical quantities. This scenario emerges by means of two scalar fields (one is present in the SB theory and the other is associated with the extra dimension) which widens the scope of the induced-matter theory. Moreover, it bears a close resemblance to the standard S\'{a}ez-Ballester scalar-tensor theory, as well as other alternative theories to general relativity, whose construction includes either a minimally or a non-minimally coupled scalar field. However, contrary to those theories, in our framework the energy momentum tensor and the scalar potential are not added by hand, but instead are dictated from the geometry. Concerning cosmological applications, our herein contribution brings a new perspective. We firstly show that the dark energy sector can be naturally retrieved within a strictly geometric perspective, and we subsequently analyze it. Moreover, our framework may provide a hint to understand the physics of lower gravity theories.