Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.

When the Higgs field is nonminimally coupled to gravity, there exists a family of spherically symmetric particlelike solutions to the field equations. These monopoles are the only globally regular and asymptotically flat distributions with finite energy of the Higgs field around compact objects. Moreover, spontaneous scalarization is strongly amplified for specific values of their mass and compactness.

Higgs inflation has received remarkable attention in the last few years due to its simplicity and predictive power. The key point of this model is the nonminimal coupling to gravity in unitary gauge. As such, this theory is in fact a scalar-tensor modification of gravity that needs to be studied also below the energy scales of inflation. Motivated by this goal, we study in great analytical and numerical detail the static and spherically symmetric solutions of the equations of motion in the presence of standard baryonic matter, called "Higgs monopoles" and presented in Füzfa et al. [Phys. Rev. Lett. 111, 12 (2013)]. These particlelike solutions may arise naturally in tensor-scalar gravity with Mexican hat potential and are the only globally regular asymptotically flat solutions with finite classical energy. In the case when the parameters of the potential are taken to be the ones of the standard model, we find that the deviations from general relativity are extremely small, especially for bodies of astrophysical size and density. This allows us to derive a simplified description of the monopole, for which the metric inside the spherical matter distribution can be approximated by the standard metric of general relativity. We study how the properties of these monopoles depend on the strength of the nonminimal coupling to gravity and on the baryonic mass and compactness. An important and original result is the existence of a mechanism of resonant amplification of the Higgs field inside the monopole that comes into play for large nonminimal coupling. We show that this mechanism might degenerate into divergences of the Higgs field that reveal the existence of forbidden combinations of radius and baryonic energy density.

Refined constraints on chameleon theories are calculated for atom-interferometry experiments, using a numerical approach consisting in solving for a four-region model the static and spherically symmetric Klein-Gordon equation for the chameleon field. By modeling not only the test mass and the vacuum chamber but also its walls and the exterior environment, the method allows to probe new effects on the scalar field profile and the induced acceleration of atoms. In the case of a weakly perturbing test mass, the effect of the wall is to enhance the field profile and to lower the acceleration inside the chamber by up to one order of magnitude. In the thin-shell regime, results are found to be in good agreement with the analytical estimations, when measurements are realized in the immediate vicinity of the test mass. Close to the vacuum chamber wall, the acceleration becomes negative and potentially measurable. This prediction could be used to discriminate between fifthforce effects and systematic experimental uncertainties, by doing the experiment at several key positions inside the vacuum chamber. For the chameleon potential V (φ) = Λ 4+α /φ α and a coupling function A(φ) = exp(φ/M ), one finds M 7 × 10 16 GeV, independently of the power-law index. For V (φ) = Λ 4 (1 + Λ/φ), one finds M 10 14 GeV. A sensitivity of a ∼ 10 −11 m/s 2 would probe the model up to the Planck scale. Finally, a proposal for a second experimental set-up, in a vacuum room, is presented. In this case, Planckian values of M could be probed provided that a ∼ 10 −10 m/s 2 , a limit reachable by future experiments. Our method can easily be extended to constrain other models with a screening mechanism, such as symmetron, dilaton and f(R) theories.