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Generic EFT-motivated beyond General Relativity gravitational wave tests and their curvature dependence: from observation to interpretation

Laura Bernard, Suvendu Giri, Luis Lehner, Riccardo Sturani

Abstract

We present a "dictionary" to expedite the identification of potential deviations in gravitational waveforms from those predicted by General Relativity (GR) during the inspiral phase of black hole binaries. Assuming deviations from GR can be described by a local Effective Field Theory (EFT) formulated in terms of curvature operators (and possibly additional scalar fields), this dictionary characterizes how deviations scale with the masses of the binary components and identifies the leading order Post-Newtonian corrections in generic theories constructed within the EFT framework. By establishing a direct connection between observations and candidate theories beyond GR, this dictionary also aids in distinguishing genuine physical effects from systematic errors. These results can be readily incorporated into essentially all existing tests for the inspiral regime and, in particular, facilitate a more efficient combination of data from multiple events.

Generic EFT-motivated beyond General Relativity gravitational wave tests and their curvature dependence: from observation to interpretation

Abstract

We present a "dictionary" to expedite the identification of potential deviations in gravitational waveforms from those predicted by General Relativity (GR) during the inspiral phase of black hole binaries. Assuming deviations from GR can be described by a local Effective Field Theory (EFT) formulated in terms of curvature operators (and possibly additional scalar fields), this dictionary characterizes how deviations scale with the masses of the binary components and identifies the leading order Post-Newtonian corrections in generic theories constructed within the EFT framework. By establishing a direct connection between observations and candidate theories beyond GR, this dictionary also aids in distinguishing genuine physical effects from systematic errors. These results can be readily incorporated into essentially all existing tests for the inspiral regime and, in particular, facilitate a more efficient combination of data from multiple events.

Paper Structure

This paper contains 28 sections, 105 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Executive summary
  3. The PN-EFT formalism
  4. Cubic gravity
  5. Feynman rules
  6. Correction to the gravitational binding potential
  7. Correction to the gravitational radiative modes
  8. Scalar-tensor gravity
  9. Feynman rules
  10. Binding potential
  11. Radiative modes
  12. Constructing general theories beyond GR
  13. 'Rules' for general case
  14. No additional scalars or gradients of Riemann
  15. With an additional scalar field
  16. ...and 13 more sections

Figures (6)

  • Figure 1: Interaction vertices at lowest orders: (a) linear scalar-matter coupling, (b) quadratic scalar-matter coupling, both coming from \ref{['eq:KS']} (c) tidal coupling coming from \ref{['eq:Stidal']}, (d) bulk $\phi^3$ interaction, and (e) bulk $\phi^2\sigma$ interaction both coming from \ref{['eq:GR-cubic']}.
  • Figure 2: Leading order coupling of radiative (wavy line) mode to a binary system of massive particles (solid straight lines) mutually interacting via potential modes (dashed lines).
  • Figure 3: Leading correction to the potential energy in (a) a cubic theory of gravity, and (b) from finite size effects.
  • Figure 4: Radiation from finite size effects (leading order).
  • Figure 5: (a) First correction to Newtonian potential from EsGB. This simply renormalizes $G_{\textrm{\scshape n}}$, Leading order correction to (b,c) the potential energy from EsGB, (d) the potential from finite size effects, and (e) the mass quadrupole.
  • ...and 1 more figures