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We calculate the PPN parameters γ and β for scalar-tensor gravity with a generic coupling function ω and scalar potential V in the Jordan conformal frame in the case of a static spherically symmetric source. Since the potential generally introduces a radial dependence to the effective gravitational constant as well as to γ and β, we discuss the issue of defining these PPN parameters and compare our expressions with previous calculations in simpler cases. We confront our results with current observational constraints on the values of γ and β and thus draw restrictions on the form of the functions ω and V around their asymptotic background values.

We compute the parametrized post-Newtonian parameter γ in the case of a static point source for multiscalar-tensor gravity with completely general nonderivative couplings and potential in the Jordan frame. Similarly to the single massive field case γ depends exponentially on the distance from the source and is determined by the length of a vector of non-minimal coupling in the space of scalar fields and its orientation relative to the mass eigenvectors. Using data from the Cassini tracking experiment, we estimate bounds on a general theory with two scalar fields. Our formalism can be utilized for a wide range of models, which we illustrate by applying it to nonminimally coupled Higgs SU(2) doublet, general hybrid metric-Palatini gravity, linear (2 −1 ) and quadratic (2 −2 ) nonlocal gravity. PACS numbers: 04.50.Kd, 04.25.Nx I. INTRODUCTIONMultiscalar-tensor gravity (MSTG) generalizes the scalar-tensor gravity (STG) of a scalar field Φ nonminimally coupled to curvature R, to the case of multiple scalar fields Φ α [1, 2]. Nonminimal couplings are typically generated by quantum corrections and arise in the effective models of higher dimensional theories. Diverse versions of MSTG appear in fundamental physics and cosmology in various constructions and under different disguises.First, there are several phenomenological motivations to consider nonminimally coupled scalars. The Standard Model Higgs field is an SU(2) complex doublet, in the case it is endowed with a nonminimal coupling to curvature also the Goldstone modes may play a role in Higgs inflation [3] and the subsequent dark energy era [4]. Otherwise a nonminimal Higgs may be paired with another nonminimal scalar (e.g. a dilaton) [5], or the inflation and dark energy could be run by two nonminimally coupled scalars [6]. More general MSTG inflation or dark energy models have N fields with noncanonical kinetic terms and arbitrary potential [1, 7-10] (also considered for stellar models [11]), or are embedded into a supergravity setup [12]. The most general multiscalar-tensor gravitational action with second order field equations includes derivative couplings and is a generalization of Horndeski's class of theories, so far worked out for the two fields case [13].Second, different proposed extensions and modifications of general relativity can be also cast into the form of MSTG by a change of variables. It is well-known that, if the gravitational lagrangian is nonlinear in curvature, f (R), or more generally f (Φ α , R), the theory is dynamically equivalent to (M)STG with the potential depending on the form of the function f [14-16]. Likewise we get an MSTG when the original lagrangian is a more complicated function of multiple arguments of R, 2R, ∇ µ R∇ µ R, Gauss-Bonnet topological term, or Weyl tensor squared [17], as each such argument can contribute a scalar nonminimally coupled to R. (A function of arbitrary curvature invariants can be also turned into scalars, but the tensor part will not generally reduce to linear R alone [18].) If the metric and connection ...

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