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Scalar-tensor theories of gravity modify General Relativity by introducing ascalar field that couples non-minimally to the metric tensor, while satisfyingthe weak-equivalence principle. These theories are interesting because theyhave the potential to simultaneously suppress modifications to Einstein'stheory on Solar System scales, while introducing large deviations in the strongfield of neutron stars. Scalar-tensor theories can be classified through thechoice of conformal factor, a scalar that regulates the coupling between matterand the metric in the Einstein frame. The class defined by a Gaussian conformalfactor with negative exponent has been studied the most because it leads tospontaneous scalarization (i.e. the sudden activation of the scalar field inneutron stars), which consequently leads to large deviations from GeneralRelativity in the strong field. This class, however, has recently been shown tobe in conflict with Solar System observations when accounting for thecosmological evolution of the scalar field. We study whether this remains thecase when the exponent of the conformal factor is positive, as well as inanother class of theories defined by a hyperbolic conformal factor. We findthat in both of these scalar-tensor theories, Solar System tests are passedonly in a very small subset of parameter space, for a large set of initialconditions compatible with Big Bang Nucleosynthesis. However, while we findthat it is possible for neutron stars to scalarize, one must carefully selectthe coupling parameter to do so, and even then, the scalar charge is typicallytwo orders of magnitude smaller than in the negative exponent case. Our studysuggests that future work on scalar-tensor gravity, for example in the contextof tests of General Relativity with gravitational waves from neutron starbinaries, should be carried out within the positive coupling parameter class.

Solar System Constraints on Scalar-Tensor Gravity with Positive Coupling Constant upon Cosmological Evolution of the Scalar Field