Constraints on Einstein-aether theory after GW170817

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, $\ensuremath{-}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}<{c}_{T}\ensuremath{-}1<7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$, which for the Einstein-aether theory implies $|{c}_{13}|\ensuremath{\le}{10}^{\ensuremath{-}15}$ with ${c}_{ij}\ensuremath{\equiv}{c}_{i}+{c}_{j}$. 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 ${\ensuremath{\sigma}}_{\ae{}}$ of neutron stars, which are not known at present in the new ranges of the parameters found in this paper.

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