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Worldline EFT treatment of quadratic and cubic gravity theories

Raghotham A Kulkarni, Rahul, Soham Bhattacharyya, Dawood Kothawala

TL;DR

This work extends the worldline EFT (WEFT) approach to modified theories of gravity by incorporating higher-curvature terms into the gravitational action and computing the resulting two-body binding potential. For quadratic gravity with an $R^2$ term, the leading effects can be removed by field redefinitions, and gauge-invariant observables show modifications only at higher PN order (3PN in the invariant energy), indicating negligible changes to conservative GR dynamics at lower PN orders. For the cubic Riemann term, the conservative dynamics acquire short-distance corrections that first appear at 2PN in intermediate expressions, but gauge-invariant binding energy calculations reveal the true physical modification comes at 6PN, consistent with a suppressed short-distance effect. The WEFT framework provides a streamlined, diagrammatic method to assess these higher-curvature corrections and motivates future work on radiative effects and gravitational-wave signatures in modified gravity scenarios.

Abstract

This paper explores modifications to General Relativity (GR) by considering higher-order curvature terms in the gravitational action, specifically focusing on the quadratic Ricci scalar and a particular cubic contraction of the Riemann tensor. These modifications introduce new interactions at short distances, potentially altering the dynamics of compact objects. We calculate the effective two-body binding potential energy for these modified theories to quantify these effects using the worldline effective field theory (WEFT) formalism. This approach allows us to systematically integrate out short-distance gravitational effects, capturing the modifications to the binding potential. Our results demonstrate how the quadratic Ricci scalar and cubic Riemann tensor terms contribute to the two-body interaction at the leading order, highlighting deviations from classical GR predictions. These findings offer insight into the potential observational signatures of modified gravity theories in binary systems and other astrophysical settings.

Worldline EFT treatment of quadratic and cubic gravity theories

TL;DR

This work extends the worldline EFT (WEFT) approach to modified theories of gravity by incorporating higher-curvature terms into the gravitational action and computing the resulting two-body binding potential. For quadratic gravity with an term, the leading effects can be removed by field redefinitions, and gauge-invariant observables show modifications only at higher PN order (3PN in the invariant energy), indicating negligible changes to conservative GR dynamics at lower PN orders. For the cubic Riemann term, the conservative dynamics acquire short-distance corrections that first appear at 2PN in intermediate expressions, but gauge-invariant binding energy calculations reveal the true physical modification comes at 6PN, consistent with a suppressed short-distance effect. The WEFT framework provides a streamlined, diagrammatic method to assess these higher-curvature corrections and motivates future work on radiative effects and gravitational-wave signatures in modified gravity scenarios.

Abstract

This paper explores modifications to General Relativity (GR) by considering higher-order curvature terms in the gravitational action, specifically focusing on the quadratic Ricci scalar and a particular cubic contraction of the Riemann tensor. These modifications introduce new interactions at short distances, potentially altering the dynamics of compact objects. We calculate the effective two-body binding potential energy for these modified theories to quantify these effects using the worldline effective field theory (WEFT) formalism. This approach allows us to systematically integrate out short-distance gravitational effects, capturing the modifications to the binding potential. Our results demonstrate how the quadratic Ricci scalar and cubic Riemann tensor terms contribute to the two-body interaction at the leading order, highlighting deviations from classical GR predictions. These findings offer insight into the potential observational signatures of modified gravity theories in binary systems and other astrophysical settings.
Paper Structure (18 sections, 92 equations)

This paper contains 18 sections, 92 equations.

Table of Contents

  1. Introduction and Motivation
  2. Worldline EFT of GR: a mini review
  3. Proof of concept: quadratic gravity
  4. Newtonian order or 0 PN
  5. $\alpha$ as a perturbing parameter
  6. Till 1 PN
  7. For all PN orders
  8. The two-particle effective Lagrangian of cubic gravity
  9. PN-1
  10. PN-2
  11. Conclusions and Discussion
  12. Future directions
  13. Acknowledgments
  14. Extra diagrams for cubic gravity at 2 PN
  15. Center of mass for cubic theories
  16. ...and 3 more sections