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, 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.

Dynamical aspects of asymmetric Eddington gravity with scalar fields

“…Inflationary models driven by multi-scalar fields are known to predict a second type of cosmological perturbations, namely isocurvature [25], especially when the fields are nonminimally coupled to gravity [17,26]. The present setup offers possible effects on these generic predictions due to the interaction of the multifields with the new degrees of freedom (curvature) through the last term of the gravitational equations (20).…”

“…In this regard, unlike fermions and gauge bosons which to some extent still require efforts to incorporate them in Eddington gravity completely, scalar fields on the other hand are found to be easily placed in metric-free actions, and allow for interesting features when applied to inflation [16,17], gravitational dark matter [18] as well as spontaneous scalarization [19] and other phenomena [20]. These models are still formulated through the strong Eddington's criteria of symmetric connection and Ricci tensor.…”

Isocurvature modes and non-Gaussianity in affine inflation

“…In what follows, we will adopt the covariant formalism to study the primordial perturbations in inflationary dynamics resulting from (14). First, each scalar of the N fields φ a (x) will be expanded around its background as φ a (x) → φ a (t) + δφ a (x).…”

“…The latter will be incorporated into the dynamics a posteriori after we generate it from the gravitational equation. As in the philosophy of affine gravity [17], the metric is generated dynamically by varying action (14) with respect to the spacetime connection Γ which yields…”

“…However, since it is highly possible that the inflationary dynamics depends on the assumed underlying theory of gravity, it is natural then to consider another quite different possibility where gravity is, rather, purely affine. Recently, affine gravitation with scalar fields has been applied to various phenomena [12][13][14][15].…”