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arXiv · 2506.00108

On the analogue of Einstein-Gauss-Bonnet theory in 3+1 dimensions

Giorgi Tukhashvili
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Abstract

Higher curvature corrections to the Einstein-Hilbert term may play an important role in probing the strong-field regime of gravity. In this letter, we demonstrate that the local effective action reproducing the trace anomaly can resemble the Einstein-Gauss-Bonnet theory in four dimensions on specific backgrounds. The two key observations support this claim: 1) the covariant equation of the trace anomaly coincides with the trace of the metric variation in Einstein-Gauss-Bonnet theory, and 2) on the FRW space-time, the Friedmann-like equations in both frameworks coincide, with this correspondence extending to the quadratic and cubic perturbations. As an intrinsically four-dimensional construct, the trace anomaly effective action emerges as a promising framework for exploring higher curvature corrections to Einstein's General Relativity in a self-consistent manner.

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Giorgi Tukhashvili. 2025-05-30. On the analogue of Einstein-Gauss-Bonnet theory in 3+1 dimensions. https://arxiv.org/abs/2506.00108

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