4D Einstein Gauss-Bonnet Gravity without a Dilaton

Abstract

A nonlocal version of Einstein-Gauss Bonnet (EGB) gravity can be generated by a procedure that follows closely the steps of the derivation of the conformal anomaly effective action. The action is obtained using a Weyl decomposition of the metric, with the conformal factor removed by a finite renormalization of the topological term. We outline the mains steps in the derivation of this action, stressing on the analogies and differences respect to the anomaly action and to the ordinary 4d EGB theory formulated as a special version of dilaton gravity. These formulations allow a systematic investigation of the nonlocal R −1 corrections to General Relativity. In the case of conformal anomaly action they are motivated by the generation of a conformal backreaction, due to the breaking of conformal symmetry in the early universe.

No logarithmic corrections to entropy in shift-symmetric Gauss-Bonnet gravity

“…Alternatively, a possibility of formulating a diffeomorphism symmetry breaking theory has been considered in[15]; see also a recent proposal for an alternative limit of Einstein gravity to two dimensions[16] 2. The recovery of area law in shift symmetric Horndeski theories was recently noted[26].…”