Bridging Dark Energy and Black Holes with EFT: Frame Transformation and Gravitational Wave Speed

TL;DR

This paper explores how effective field theory parameters for dark energy transform between frames and affect black hole perturbations, revealing potential deviations in gravitational wave speeds near black holes.

Contribution

It provides a detailed analysis of frame transformations in EFT of dark energy and investigates their impact on black hole perturbations and gravitational wave speeds.

Findings

Deviations from luminal gravitational wave speed occur near black holes.

Radial and angular perturbation speeds differ due to background extrinsic curvature.

Frame transformations connect cosmological and black hole EFT constraints.

Abstract

Typically, constraints on parameters of the effective field theory (EFT) of dark energy have been obtained in the Jordan frame, where matter fields are minimally coupled to gravity. To connect these constraints with those of the EFT of black hole perturbations with a timelike scalar profile, it is necessary to perform a frame transformation on the EFT in general. In this paper, we study the conformal/disformal transformation of EFT parameters on an arbitrary background. Furthermore, we explore the effect of an EFT operator $M_6(r) \bar{\sigma}^{\mu}_{\nu} \delta K^{\nu}_{\alpha} \delta K^{\alpha}_{\mu}$, which is elusive to the LIGO/Virgo bound on gravitational-wave speed, on the dynamics of odd-parity black hole perturbations. Intriguingly, a deviation from luminal propagation shows up only in the vicinity of the black hole, and the speeds of perturbations in the radial and angular directions are different in general due to the traceless part $\bar{\sigma}^\mu_\nu$ of the background extrinsic curvature. This study establishes an important link between cosmological constraints and those obtained in the black hole regime.