Generalized Scale Invariant Gravity

TL;DR

This paper introduces a generalized scalar-tensor gravity theory with a negative kinetic scalar field, demonstrating that Einstein gravity emerges as a ground state after quantum corrections, with implications for cosmology and experimental constraints.

Contribution

It proposes a new scalar-tensor gravity model with a negative kinetic term, analyzes its quantum corrections, and shows Einstein gravity as a ground state, linking scale invariance to cosmological observations.

Findings

Scale symmetry is broken dynamically.

Einstein gravity is the ground state after quantum corrections.

Time-delay experiments constrain the universe close to the ground state.

Abstract

We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a pure gravity theory without matter, the scale symmetric phase represents an equivalent class of gravity theories, which the Einstein gravity plus a cosmological constant belongs to under a special gauge choice. The one-loop quantum correction of the theory is calculated by using the Vilkovisky-DeWitt's method. We find that the scale symmetry is broken dynamically, and that the Einstein gravity is the ground state of the broken phase. We also briefly discuss the consequent cosmological implications. It is shown that the time-delay experiment restricts the present universe to be very close to the ground state.