Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Testing Dark Energy with Black Hole Ringdown

Laurens Smulders, Johannes Noller, Sergi Sirera

Abstract

We show that dynamical dark energy theories can imprint $O(1)$ modifications on the quasi-normal mode (QNM) spectrum characterising black hole ringdown. The time dependence of dynamical dark energy naturally gives rise to cosmological 'hair' around a black hole. Taking the cubic Galileon as a concrete example, which admits the only known stable solution of this kind, we parametrically connect the cosmological and black hole regimes, derive the induced QNM shifts and forecast the resulting dark energy constraints. We find that the dark energy field profile can be constrained with an accuracy of up to $10^{-2}$ for LVK and $10^{-4}$ for LISA.

Testing Dark Energy with Black Hole Ringdown

Abstract

We show that dynamical dark energy theories can imprint modifications on the quasi-normal mode (QNM) spectrum characterising black hole ringdown. The time dependence of dynamical dark energy naturally gives rise to cosmological 'hair' around a black hole. Taking the cubic Galileon as a concrete example, which admits the only known stable solution of this kind, we parametrically connect the cosmological and black hole regimes, derive the induced QNM shifts and forecast the resulting dark energy constraints. We find that the dark energy field profile can be constrained with an accuracy of up to for LVK and for LISA.
Paper Structure (11 sections, 39 equations, 4 figures, 1 table)

This paper contains 11 sections, 39 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Stable Black Holes with cosmological hair
  3. Connecting cosmological and black hole solutions
  4. Quasi-normal mode spectra
  5. Forecasted Constraints and testing dark energy
  6. Conclusions
  7. Equations of motion
  8. Regge-Wheeler gauge
  9. Modified Regge-Wheeler and Zerilli equations
  10. Fisher information analysis
  11. Inspiral/merger constraints on the remnant mass

Figures (4)

  • Figure 1: Values for the hair parameter $\beta$ obtained using the shooting methodBabichev:2016fbgEmond:2019myxSmulders:2026 for a range of scalar velocities $q/q_0$ and example $Hr_s$ values. We see an excellent fit with a linear dependence on $q/q_0$ given by equation \ref{['eq:BetaFittingFormula']}, and no leading order dependence on $Hr_s$.
  • Figure 2: The quasi-normal mode (QNM) frequencies for different values of $\beta$, shown for $\ell = 2,3,4$. M is the (remnant) black hole mass and $\omega_I$ and $\omega_R$ are the imaginary and real parts of the complex QNM frequency $\omega$. Cosmological hair induced deviations from the GR limit $\beta = 1$ leads to QNM frequency modifications of up to $\sim 40 \; \%$. Here, using \ref{['eq:BetaFittingFormula']}, $\beta\sim2$ is the maximum $\beta$ for which $q$ satisfies the bound formulated in \ref{['eq:qBound']}, ensuring homogeneity on large scales.
  • Figure 3: Forecasted constraints on the black hole hair parameter $\beta$ as a function of the uncertainty in the inspiral/merger-inferred remnant mass $\sigma_M/M$ and the ringdown SNR $\rho$ -- see Eq. \ref{['eq:error-beta']}. We show the estimated precision of current LVK and forecasted future measurements.
  • Figure 4: Fisher ellipses in the $(M, \beta)$ plane, illustrating the complete degeneracy between the two. Independent prior knowledge on $M$ can effectively break the degeneracy, with the final constraint limited by the SNR of the ringdown signal.