Gravity in 2T-Physics

TL;DR

This paper develops a gravitational theory in 2T-physics with two time dimensions, showing how General Relativity emerges as a shadow in lower dimensions and exploring implications for cosmology and fundamental constants.

Contribution

It constructs a consistent 2T-physics action for gravity, linking higher-dimensional fields to 4D physics and revealing the dynamical nature of the gravitational constant.

Findings

Gravity in 2T-physics reproduces classical General Relativity in lower dimensions.

The gravitational constant is a shadow of a dilaton field, varying across cosmological phase transitions.

The framework is consistent with previous 2T-physics models of the Standard Model.

Abstract

The field theoretic action for gravitational interactions in d+2 dimensions is constructed in the formalism of 2T-physics. General Relativity in d dimensions emerges as a shadow of this theory with one less time and one less space dimensions. The gravitational constant turns out to be a shadow of a dilaton field in d+2 dimensions that appears as a constant to observers stuck in d dimensions. If elementary scalar fields play a role in the fundamental theory (such as Higgs fields in the Standard Model coupled to gravity), then their shadows in d dimensions must necessarily be conformal scalars. This has the physical consequence that the gravitational constant changes at each phase transition (inflation, grand unification, electro-weak, etc.), implying interesting new scenarios in cosmological applications. The fundamental action for pure gravity, which includes the spacetime metric, the dilaton and an additional auxiliary scalar field all in d+2 dimensions with two times, has a mix of gauge symmetries to produce appropriate constraints that remove all ghosts or redundant degrees of freedom. The action produces on-shell classical field equations of motion in d+2 dimensions, with enough constraints for the theory to be in agreement with classical General Relativity in d dimensions. Therefore this action describes the correct classical gravitational physics directly in d+2 dimensions. Taken together with previous similar work on the Standard Model of particles and forces, the present paper shows that 2T-physics is a general consistent framework for a physical theory.