Probing the speed of gravity with LVK, LISA, and joint observations

Abstract

Theories of dark energy that affect the speed of gravitational waves $$c_{\textrm{GW}}$$ c GW on cosmological scales naturally lead to a frequency-dependent transition of that speed close to the LIGO/Virgo/KAGRA (LVK) band. While observations such as GW170817 assure us that $$c_{\textrm{GW}}$$ c GW is extremely close to the speed of light in the LVK band, a frequency-dependent transition below the LVK band is a smoking-gun signal for large classes of dynamical dark energy theories. Here we discuss (1) how the remnants of such a transition can be constrained with observations in the LVK band, (2) what signatures are associated with such a transition in the LISA band, and (3) how joint observations in the LVK and LISA bands allow us to place tight constraints on this transition and the underlying theories. We find that deviations of $$c_{\textrm{GW}}$$ c GW can be constrained down to a level of $$\sim 10^{-17}$$ ∼ 10 - 17 in the LVK and LISA bands even for mild frequency-dependence, much stronger than existing bounds for frequency-independent $$c_{\textrm{GW}}\ne c$$ c GW ≠ c . We use the strain data from GW170817 to bound the deviation of $$c_{\textrm{GW}}$$ c GW to be less than $$10^{-17}$$ 10 - 17 at 100 Hz and less than $$10^{-18}$$ 10 - 18 at 500 Hz. We also identify a particularly interesting type of transition in between the LVK and LISA bands and show how multi-band observations can constrain this further. Finally, we discuss what these current and forecasted constraints imply for the underlying dark energy theories.

Testing gravitational wave propagation with multiband detections

“…In the present work we instead perform a FIM analysis, which allows us to make statements about simultaneous constraints on regular and modified gravity parameters, and their degeneracies. The conclusions presented here are nevertheless in perfect agreement with those of [49].…”

“…As described in [49], a deviation of δc/c EM = 3 × 10 −15 would be sufficient to shift by 2 minutes the coalescence time t c in the LVK band. Given our FIM forecast on t c for GW150914-like events, in such a case we will be almost certain to detect the time shift with respect to the LISA prediction.…”

“…During the last parts of this analysis, we became aware of similar methods and results being derived in [49]. The precise details of that analysis differ from the current work in places: for example, the authors of [49] consider a 'distinguishability criterion' to assess if the time-shift of their waveforms induced by varying c T is recognisable.…”

“…During the last parts of this analysis, we became aware of similar methods and results being derived in [49]. The precise details of that analysis differ from the current work in places: for example, the authors of [49] consider a 'distinguishability criterion' to assess if the time-shift of their waveforms induced by varying c T is recognisable. In the present work we instead perform a FIM analysis, which allows us to make statements about simultaneous constraints on regular and modified gravity parameters, and their degeneracies.…”

“…Any modification of the dispersion relation can be already strongly constrained at LVK frequency scales, as proved in many analysis [54][55][56][57][58][59]: see [49] for the most recent strongest constraints. We shall therefore take an agnostic approach and focus our attention on the extreme situation where the speed of GWs is considered to be exactly luminal at LVK scales and precisely constant (but non-luminal) at LISA scales, with a sharp transition in between.…”