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Register a new userInducing Gravity From Connections and Scalar Fields
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Hemza Azri
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We propose an approach to induced gravity, or Sakharovs 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 Newtons 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.
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In Eddington gravity, the action principle involves only the symmetric parts of the connection and the Ricci tensor, with a metric that emerges proportionally to the latter. Here, we relax this symmetric character, prolong the action with the antisymmetric parts of the Ricci term, and allow for various couplings with scalar fields. We propose two possible invariant actions formed by distinct combinations of the independent Ricci tensors and show that the generated metric must involve an additional antisymmetric part due to the relaxation of the symmetrization property. The comprehensive study shows that the second curvature influences the dynamics of the connection, hence its solution in terms of the metric, and the evolution of the scalar fields. These new dynamical features are expected to stand viable and to have interesting implications in domains where scalar fields are indispensable.
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