Non-Gravitating Scalars and Spacetime Compactification

TL;DR

This paper explores how partially gravitating scalar fields can induce spontaneous compactification of extra dimensions in higher-dimensional spacetimes, leading to factorizable geometries with controlled size and shape.

Contribution

It introduces the concept of partially gravitating scalar fields and demonstrates their role in dynamical spacetime compactification with a detailed analysis of scalar field VEV effects.

Findings

Nonzero scalar VEV leads to spontaneous compactification.

Scalar fields with zero VEV do not induce compactification.

The size and shape of extra dimensions depend on scalar field dynamics.

Abstract

We discuss role of partially gravitating scalar fields, scalar fields whose energy-momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincare invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its VEV is zero the higher dimensional spacetime is completely flat and there is no compactification effect at all. On the other hand, when its VEV is nonzero the extra dimensions get spontaneously compactified. The compactification process is such that a bulk cosmological constant is utilized for curving the extra dimensions.