Black hole ringdown as a probe for dark energy

Abstract

Under the assumption that a dynamical scalar field is responsible for the current acceleration of the Universe, we explore the possibility of probing its physics in black hole merger processes with gravitational wave interferometers. Remaining agnostic about the microscopic physics, we use an effective field theory approach to describe the scalar dynamics. We investigate the case in which some of the higher derivative operators, that are highly suppressed on cosmological scales, instead become important on typical distances for black holes. If a coupling to the Gauss-Bonnet operator is one of them, a non-trivial background profile for the scalar field can be sourced in the surrounding of the black hole, resulting in a potentially large amount of 'hair'. In turn, this can induce sizeable modifications to the spacetime geometry or a mixing between the scalar and the gravitational perturbations. Both effects will ultimately translate into a modification of the quasi-normal mode spectrum in a way that is also sensitive to other operators besides the one sourcing the scalar background. The presence of deviations from the predictions of general relativity in the observed spectrum can therefore serve as a window onto dark energy physics.

Cosmological constraints on dark energy in light of gravitational wave bounds

“…In this context at least some solar system tests would therefore not even test the cosmological EFT anymore, but depend on the precise properties of the UV completion. If instead one insists on solar system tests as well as strong field tests around black holes to be within the regime of validity of the cosmological EFT, one should require Λ UV 1 km −1 , translating into Λ 10 5 Λ 3 [88]. This would of course automatically satisfy both GW priors, but also bring down the previously discussed Vainshtein radius to ∼ 10 10 km, i.e.…”

“…11 Note that, if this coupling is not of gravitational strength, but modified by a dimensionless coupling constant δ , this will enter in (23) as an extra δ 1/3 factor [88]. If the coupling is indeed only generated via de-mixing the α B -induced scalar-tensor mixing of cosmological perturbations, then we have δ ∼ α B .…”

“…While Vainshtein screening may still be present to an extent and associated with higher-derivative interactions inside G 2 (e.g. of the k-essence X n type [76-79] -see [80][81][82][83] for screening-related discussions in this setup) and Chameleon screening [84,85] can be associated with the conformal f (φ ) coupling 8 (see [87] for a review of Chameleon-related constraints), here instead we wish to explore another option: Following [88] we want to understand the above GW priors (on the speed of GWs and on the absence of GW-induced dark energy instabilities) as constraints on the strong coupling scale Λ of general Horndeski theories and understand what this implies for that scale and for related screening mechanisms.…”

“…When raising Λ, contributions from the associated operators will generically become suppressed at the cosmological level, but may still contribute at smaller scales. For example, in [88] it was shown that constraints on α T can be satisfied in this way, while still yielding observable O(1) modifications around black hole space times.…”

“…where we keep the lowest powers of Λ 3 /Λ. 10 The α T constraint can therefore be satisfied by setting Λ 10 3 Λ 3 [88], where in the EFT-spirit we implicitly assume that all other dimensionless coefficients in the theory are O(1). Raising Λ at this level also automatically yields |α M + α B | ∼ 10 −9 , very comfortably satisfying the 10 −2 level constraint from requiring the absence of GW-induced dark energy instabilities.…”