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Dynamical 4-D Gauss-Bonnet action from matter-graviton interactions in a curved background

Apurv Keer, S. Shankaranarayanan

Abstract

The Glavan-Lin proposal for 4D Einstein-Gauss-Bonnet (EGB) gravity introduces a singular dimensional scaling to bypass Lovelock's theorem, though its fundamental origin remains debated. In this work, we demonstrate that this specific dimension-dependent scaling naturally emerges from the one-loop self-energy corrections of gravitons. By employing real-space techniques to evaluate graviton interactions with minimally coupled scalar and electromagnetic fields in a de Sitter background, we show that the $1/(D-4)$ pole universally generates a dynamical Gauss-Bonnet term. This confirms that the scaling is not an ad-hoc classical limit but a necessary consequence of quantum field-theoretic renormalization. Furthermore, canceling the remaining divergences strictly requires the inclusion of quadratic curvature counterterms, specifically Weyl-squared and $R^2$ invariants. We discuss the implications of this in the early-Universe and consequences in strong gravity regime.

Dynamical 4-D Gauss-Bonnet action from matter-graviton interactions in a curved background

Abstract

The Glavan-Lin proposal for 4D Einstein-Gauss-Bonnet (EGB) gravity introduces a singular dimensional scaling to bypass Lovelock's theorem, though its fundamental origin remains debated. In this work, we demonstrate that this specific dimension-dependent scaling naturally emerges from the one-loop self-energy corrections of gravitons. By employing real-space techniques to evaluate graviton interactions with minimally coupled scalar and electromagnetic fields in a de Sitter background, we show that the pole universally generates a dynamical Gauss-Bonnet term. This confirms that the scaling is not an ad-hoc classical limit but a necessary consequence of quantum field-theoretic renormalization. Furthermore, canceling the remaining divergences strictly requires the inclusion of quadratic curvature counterterms, specifically Weyl-squared and invariants. We discuss the implications of this in the early-Universe and consequences in strong gravity regime.
Paper Structure (12 sections, 49 equations, 2 figures)

This paper contains 12 sections, 49 equations, 2 figures.

Table of Contents

  1. Introduction
  2. One loop graviton self energy
  3. One loop graviton self energy in flat spacetime
  4. Momentum-space approach
  5. Real-space approach
  6. Scalar contribution to Graviton self-energy in de Sitter
  7. Graviton self-energy correction in de Sitter
  8. Comparison with the Gauss-Bonnet term
  9. Photon contribution to graviton self-energy in de Sitter
  10. Implications for the Early Universe
  11. Discussion
  12. de Sitter space

Figures (2)

  • Figure 1: One-loop Feynman diagram describing the self-energy correction to the graviton propagator due to a massless scalar field loop.
  • Figure 2: One-loop Feynman diagram describing the self-energy correction to the graviton propagator due to a photon.