[Paper Review] Effective speed of gravitational waves

Antonio Enea Romano|arXiv (Cornell University)|Nov 10, 2022

Pulsars and Gravitational Waves Research6 references4 citations

TL;DR

This paper develops a model-independent framework for studying gravitational wave (GW) propagation in modified gravity and dark energy theories using an effective stress-energy-momentum tensor and effective action approach. It derives frequency- and polarization-dependent effective GW speeds and Planck masses, showing that luminosity distance ratios between GWs and electromagnetic waves can constrain these effective parameters, with observable signatures in bright and dark siren events.

ABSTRACT

We derive an effective equation and action for the propagation of gravitational waves (GW), encoding the effects of interaction and self-interaction in a time, frequency and polarization dependent effective speed. In terms of an appropriately defined effective metric, the effective action takes the form a massless Klein-Gordon action. This effective approach predicts that for theories with matter coupled to the Einstein frame metric the ratio between gravitational and electromagnetic (EM) luminosity distance depends on the effective speed, while for Jordan frame matter coupling it depends on the effective Planck mass. We discuss how the frequency and polarization dependence of the GW-EM distance ratio provides a new test of general relativity and its modifications, and more in general of the interaction of GWs with other fields.

Motivation & Objective

• To develop a model-independent approach for analyzing gravitational wave propagation in modified gravity and dark energy theories.
• To generalize the effective field theory of dark energy to include arbitrary matter Lagrangians and higher-order interactions.
• To derive effective equations for GW propagation that account for frequency- and polarization-dependent effects beyond quadratic actions.
• To connect observable luminosity distance ratios between GWs and electromagnetic waves to effective GW speed and Planck mass.
• To enable observational constraints using bright and dark siren data across multiple redshifts and frequencies.

Proposed method

• Derives an effective action in both Einstein and Jordan frames, incorporating higher-order interaction terms via effective field theory.
• Uses the scalar-vector-tensor (SVT) decomposition of metric and effective stress-energy-momentum tensor perturbations to maintain model independence.
• Introduces an effective GW speed and effective Planck mass that can depend on time, frequency, and polarization due to anisotropic source terms.
• Applies the effective stress-energy-momentum tensor (EST) approach to encode higher-order effects not captured in quadratic actions.
• Derives a modified wave equation for GWs with a friction term dependent on the effective speed and Planck mass, valid in any conformal frame.
• Proposes phenomenological parametrizations for the luminosity distance ratio to test observational constraints from GW-EM counterparts.

Experimental results

Research questions

• RQ1 How can the propagation of gravitational waves be described in a model-independent way beyond quadratic actions?
• RQ2 What are the observable consequences of frequency- and polarization-dependent effective GW speeds and Planck masses?
• RQ3 How do luminosity distance ratios between GWs and electromagnetic waves constrain effective parameters in modified gravity and dark energy models?
• RQ4 In what way do Einstein and Jordan frame formulations differ in their treatment of effective GW speed and Planck mass?
• RQ5 Can dark siren observations provide tighter constraints on effective GW speed than bright siren events?

Key findings

• The effective GW speed and Planck mass can depend on frequency and polarization due to higher-order interaction terms, even in theories with constant vacuum values.
• The luminosity distance ratio between GWs and EM waves becomes frequency- and polarization-dependent due to the effective friction term in the wave equation.
• For Einstein frame matter coupling, the luminosity distance ratio depends on the effective GW speed; for Jordan frame coupling, it depends on the effective Planck mass.
• The observed GW170817 event imposes tight constraints on the low-redshift effective GW speed at LIGO-Virgo frequencies.
• Phenomenological parametrizations such as Eq. (42) and Eq. (43) can describe transitions in the luminosity distance ratio with scale-dependent features.
• Combining data from multi-band GW detectors like LISA, Einstein Telescope, and Cosmic Explorer will enable full constraints on the model-independent effective parameters.