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PPN parameters in gravitational theory with nonminimally derivative coupling

The nonminimal coupling of the kinetic term to Einstein's tensor helps the implementation of inflationary models due to the gravitationally enhanced friction. We calculate the parametrized post-Newtonian (PPN) parameters for the scalar--tensor theory of gravity with nonminimally derivative coupling. We find that under experimental constraint from the orbits of millisecond pulsars in our galaxy, the theory deviates from Einstein's general relativity in the order of $10^{-20}$, and the effect of the nonminimal coupling is negligible if we take the scalar field as dynamical dark energy. With the assumed conditions that the background scalar field is spatially homogeneous and evolves only on cosmological timescales and the contribution to stress--energy in the solar system from the background scalar field is subdominant, the scalar field is required to be massless.