Inducing Gravity From Connections and Scalar Fields

TL;DR

This paper introduces a novel approach to induced gravity starting from an affine spacetime with scalar fields, deriving metric gravity and Newton's constant from a pure affine action at both classical and quantum levels.

Contribution

It presents a new framework where the metric structure emerges from a primary affine theory, unifying classical and quantum induced gravity mechanisms.

Findings

Einstein-Hilbert action arises from scalar field potential energy.

Gravity scale is induced via one-loop quantum corrections.

The approach naturally produces metric structure without imposing it a priori.

Abstract

We propose an approach to induced gravity, or Sakharov's "metrical elasticity", which requires only an affine spacetime that accommodates scalar fields. The setup provides the induction of metric gravity from a "pure affine" action, and it is established in two possible ways: (i) at the classical level, Einstein-Hilbert action arises with both, metric and Newton's constant, from the nonzero potential energy of the background field (ii) at the quantum level (quantized matter), gravity scale is induced from the one-loop effective action by integrating out the scalar degrees of freedom. In the former, the cosmological constant is absorbed leading to the gravitational sector, however, the fact remains that quantum corrections induce a large cosmological constant. This new approach adds a crucial feature to induced gravity which is the fact that the metric structure is not imposed from the scratch, but it is an outcome of the primary theory.