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Effects of massive spin-2 fields on gravitational wave propagation

Jose A. R. Cembranos, Álvaro Cendal, Hector Villarrubia-Rojo

TL;DR

The work examines how massive spin-2 fields modify gravitational wave propagation in extensions of GR, framing the problem within a phenomenological coupled-mode picture. An analytical transfer function is derived in the ultrarelativistic limit using a WKB approach, linking the modified waveform to the GR prediction via a scale- and redshift-dependent amplitude and phase. A box-like detector model and the Lindblom criterion yield tractable detectability bounds, which are then applied to current LVK data (via GWTC-4) and to future missions (ET/CE and LISA) using simulated event catalogs. The results indicate that GW observations can probe extremely small masses ($m \ll 10^{-20}$ eV) under optimistic assumptions, with future detectors expanding sensitivity across broader parameter space, offering a practical route to testing massive spin-2 gravity through GW propagation.

Abstract

Massive spin-2 fields in addition to the standard massless graviton arise naturally in extensions of General Relativity, such as massive bigravity or models with extra dimensions. This work explores the observational signatures of these fields on the propagation of gravitational waves. Adopting a phenomenological framework consistent with such theories, we derive an analytical transfer function in the ultrarelativistic limit and establish detectability bounds. Finally, we provide forecasts for the accessible parameter space using current and future gravitational wave detectors.

Effects of massive spin-2 fields on gravitational wave propagation

TL;DR

The work examines how massive spin-2 fields modify gravitational wave propagation in extensions of GR, framing the problem within a phenomenological coupled-mode picture. An analytical transfer function is derived in the ultrarelativistic limit using a WKB approach, linking the modified waveform to the GR prediction via a scale- and redshift-dependent amplitude and phase. A box-like detector model and the Lindblom criterion yield tractable detectability bounds, which are then applied to current LVK data (via GWTC-4) and to future missions (ET/CE and LISA) using simulated event catalogs. The results indicate that GW observations can probe extremely small masses ( eV) under optimistic assumptions, with future detectors expanding sensitivity across broader parameter space, offering a practical route to testing massive spin-2 gravity through GW propagation.

Abstract

Massive spin-2 fields in addition to the standard massless graviton arise naturally in extensions of General Relativity, such as massive bigravity or models with extra dimensions. This work explores the observational signatures of these fields on the propagation of gravitational waves. Adopting a phenomenological framework consistent with such theories, we derive an analytical transfer function in the ultrarelativistic limit and establish detectability bounds. Finally, we provide forecasts for the accessible parameter space using current and future gravitational wave detectors.
Paper Structure (8 sections, 25 equations, 4 figures)

This paper contains 8 sections, 25 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Propagation of massless and massive tensor modes
  3. Relating GR and modified coupling constants
  4. Propagation of interaction eigenstates and transfer function
  5. Detectability criterion
  6. Analytical approach: box-like detector approximation
  7. Detectability forecast
  8. Summary and conclusions

Figures (4)

  • Figure 1: Function $\alpha(z)$ as a function of the redshift $z$. Vertical lines indicate the redshifts of GW170817 (the closest event recorded), GW150914, and GW190403 (the farthest event recorded) for reference.
  • Figure 2: Detectability bounds for different test events, computed both numerically (solid) and using the analytical approximation \ref{['eq:analytical_approximation']} (dotted).
  • Figure 3: Detectability forecast for the LVK network (gold), ET+CE network (light blue), and LISA (pink).
  • Figure 4: Examples of the effects of the massive spin-2 field on GW150914-like waveforms for different values of the mass $m$, fixing $\tan \theta = 0.5$, both in the frequency (left) and time (right) domains. The black line corresponds to the original GR waveform. Inset shows the position of $(m, \tan \theta)$ in the detectability forecast of LVK from GWTC-4 events.