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

Abstract

Theories of dark energy that affect the speed of gravitational waves 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 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 GW can be constrained down to a level of ∼ 10 −17 in the LVK and LISA bands even for mild frequency-dependence, much stronger than existing bounds for frequency-independent c GW = c. We use the strain data from GW170817 to bound the deviation of c GW to be less than 10 −17 at 100 Hz and less than 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.

The effects of dark energy on the propagation of gravitational waves

“…where k * A is the scale at which a transition takes place, γ A controls the size of the change, and σ A the sharpness of the transition. The GW170817 observations impose the condition that the transition scale k * should be outside the range probed by LIGO-Virgo [17,31]. Other constraints on the cT,A can be obtained from the waveform [31], since stretching or squeezing is expected, and they could be combined with those on the luminosity distance given in eq.…”