Geometry and Symmetry Structures in 2T Gravity

TL;DR

This paper explores how 2T-gravity in higher dimensions predicts 1T General Relativity with a Weyl symmetry, revealing new constraints and geometric structures that could test 2T-physics and explain the origin of fundamental constants.

Contribution

It develops the geometric and symmetry structures of 2T-gravity, showing how 1T GR with Weyl symmetry emerges from higher-dimensional reparametrizations and constraints.

Findings

Weyl symmetry in 1T arises from coordinate reparametrization in 2T.

Gravitational constant linked to vacuum values of scalars and varies after cosmic transitions.

Higher-dimensional structures include 'prolongations' determined by 1T shadows.

Abstract

2T-gravity in d+2 dimensions predicts 1T General Relativity (GR) in d dimensions, augmented with a local scale symmetry known as the Weyl symmetry in 1T field theory. The emerging GR comes with a number of constraints, particularly on scalar fields and their interactions in 1T field theory. These constraints, detailed in this paper, are footprints of 2T-gravity and could be a basis for testing 2T-physics. Some of the conceptually interesting consequences of the "accidental" Weyl symmetry include that the gravitational constant emerges from vacuum values of the dilaton and other Higgs-type scalars and that it changes after every cosmic phase transition (inflation, grand unification, electroweak phase transition, etc.). We show that this consequential Weyl symmetry in d dimensions originates from coordinate reparametrization, not from scale transformations, in the d+2 spacetime of 2T-gravity. To recognize this structure we develop in detail the geometrical structures, curvatures, symmetries, etc. of the d+2 spacetime which is restricted by a homothety condition derived from the action of 2T-gravity. Observers that live in d dimensions perceive GR and all degrees of freedom as shadows of their counterparts in d+2 dimensions. Kaluza-Klein (KK) type modes are removed by gauge symmetries and constraints that follow from the 2T-gravity action. However some analogs to KK modes, which we call "prolongations" of the shadows into the higher dimensions, remain but they are completely determined, up to gauge freedom, by the shadows in d dimensions.