Abstract
General relativity has been very successful since its proposal more than a century ago. However, various cosmological observations and theoretical consistency still motivate us to explore extended gravity theories. Horndeski gravity stands out as one attractive theory by introducing only one scalar field. Here we formulate the post-Newtonian effective field theory of Horndeski gravity and investigate the conservative dynamics of inspiral compact binary systems. We calculate the leading effective Lagrangian for a compact binary and obtain the periastron advance per period. In particular, we apply our analytical calculation to two binary systems, PSR B 1534+12 and PSR J0737-3039, and constrain the relevant model parameters. This theoretical framework can also be systematically extended to higher orders.
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