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Constraining the Cosmological Evolution of Post-Newtonian Parameters with Gravitational Wave Signals from Compact Binary Inspirals

Oliver Pitt, Timothy Clifton

Abstract

Gravitational waves from compact binary inspirals offer a new opportunity to constrain the cosmological time dependence of gravitational coupling parameters, due to the high precision of the observations themselves as well as the significant cosmological redshifts at which such systems exist. We calculate theory-independent equations of motion for compact objects in a binary system, implementing a new approach to sensitivities, and subsequently determine the gravitational wave signal that one should expect to measure from their inspiral. Expressions for the wave phase and amplitude are derived in terms of post-Newtonian gravitational coupling parameters, radiative flux parameters, and compact body sensitivities. These results complement recent attempts to gain theory-independent constraints on the time-evolution of gravitational coupling parameters from cosmological probes, and represent a new opportunity to constrain modified gravity with gravitational wave data.

Constraining the Cosmological Evolution of Post-Newtonian Parameters with Gravitational Wave Signals from Compact Binary Inspirals

Abstract

Gravitational waves from compact binary inspirals offer a new opportunity to constrain the cosmological time dependence of gravitational coupling parameters, due to the high precision of the observations themselves as well as the significant cosmological redshifts at which such systems exist. We calculate theory-independent equations of motion for compact objects in a binary system, implementing a new approach to sensitivities, and subsequently determine the gravitational wave signal that one should expect to measure from their inspiral. Expressions for the wave phase and amplitude are derived in terms of post-Newtonian gravitational coupling parameters, radiative flux parameters, and compact body sensitivities. These results complement recent attempts to gain theory-independent constraints on the time-evolution of gravitational coupling parameters from cosmological probes, and represent a new opportunity to constrain modified gravity with gravitational wave data.

Paper Structure

This paper contains 14 sections, 79 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Theoretical Foundations
  3. Parametrized Post-Newtonian (PPN) Theory
  4. Sensitivities of Compact Bodies
  5. Theory-Independent Gravitational Luminosity
  6. Theory-Independent Equations of Motion for Compact Objects
  7. A Single Sensitive Body
  8. Two Sensitive Bodies
  9. Post-Newtonian Sensitivities
  10. Gravitational Wave Phase and Amplitude
  11. Example: Scalar-Tensor Gravity
  12. Observational Constraints
  13. Discussion
  14. Concluding remarks

Figures (1)

  • Figure 1: Constraints on $\beta/\alpha^2-1$ as a function of cosmological redshift, for the simple relation in Equation (\ref{['phi2simp']}), and the data from Table \ref{['obstab']}. Shaded regions correspond to $68\%$ and $95\%$ confidence intervals, with linear regression having been performed to maximize a Gaussian likelihood function. We have taken $H_0\simeq 73\, {\rm km} \, {\rm s}^{-1} {\rm Mpc}^{-1}$riess2022comprehensive, and have used $\gamma \simeq \alpha$ over cosmic history thomas2024constraining.