In this paper, we carry out a systematic analysis of the theoretical and observational constraints on the dimensionless coupling constants $c_i$ ($i=1$, 2, 3, 4) of the Einstein-aether theory, taking into account the events GW170817 and GRB 170817A. The combination of these events restricts the deviation of the speed $c_T$ of the spin-2 graviton to the range, $-3\times {10}^{-15}<c_T-1<7\times {10}^{-16}$, which for the Einstein-aether theory implies $|c_{13}|\le {10}^{-15}$ with $c_{ij}\equiv c_i+c_j$. The rest of the constraints are divided into two groups: those on the ($c_1$, $c_{14}$)-plane and those on the ($c_2$, $c_{14}$)-plane, except the strong-field constraints. The latter depend on the sensitivities ${\sigma }_{\ae }$ of neutron stars, which are not known at present in the new ranges of the parameters found in this paper.

Black hole spectroscopy with gravitational waves is an important tool to measure the mass and spin of astrophysical black holes and to test their Kerr nature. Next-generation ground- and space-based detectors will observe binary black hole mergers with large signal-to-noise ratios and perform spectroscopy routinely. It was recently shown that small perturbations due, e.g., to environmental effects (the “flea”) to the effective potential governing gravitational-wave generation and propagation in black hole exteriors (the “elephant”) can lead to arbitrarily large changes in the black hole’s quasinormal spectrum, including the fundamental mode, which is expected to dominate the observed signal. This raises an important question: is the black hole spectroscopy program robust against perturbations? We clarify the physical behavior of time-domain signals under small perturbations in the potential, and we show that changes in the amplitude of the fundamental mode in the prompt ringdown signal are parametrically small. This implies that the fundamental quasinormal mode extracted from the observable time-domain signal is stable against small perturbations. The stability of overtones deserves further investigation.

We consider the possibility that the massive graviton is a viable candidate for dark matter in the context of bimetric gravity. We first derive the energy-momentum tensor of the massive graviton and show that it indeed behaves as that of dark matter fluid. We then discuss a production mechanism and the present abundance of massive gravitons as dark matter. Since the metric to which ordinary matter fields couple is a linear combination of the two mass eigenstates of bigravity, production of massive gravitons, i.e., the dark matter particles, is inevitably accompanied by generation of massless gravitons, i.e., the gravitational waves. Therefore, in this scenario some information about dark matter in our Universe is encoded in gravitational waves. For instance, if LIGO detects gravitational waves generated by the preheating after inflation, then the massive graviton with the mass of $\sim 0.01\mathrm{GeV}$ is a candidate for dark matter.