Inducing gravity from connections and scalar fields

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, the 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.