The environment dependent dilaton in the laboratory and the solar system

We consider the environment-dependent dilaton in the laboratory and the solar system and derive approximate analytical solutions to the field theory equations of motion in the presence of a one or two mirror system or a sphere. The solutions obtained herein can be applied to qBOUNCE experiments, neutron interferometry and for the calculation of the dilaton field induced "Casimir force" in the Cannex experiment as well as for Lunar Laser Ranging. They are typical of the Damour-Polyakov screening mechanism whereby deviations from General Relativity are suppressed by a vanishingly small direct coupling of the dilaton to matter in dense environments. We specifically focus on dilaton models which are compatible with the late time acceleration of the expansion of the Universe, i.e. the cosmological dilaton. We show how future laboratory experiments will essentially test a region of parameter space with $$ where $$ is the quadratic coupling strength of the dilaton to matter and $$ is the steepness of the exponential runaway potential. Current constraints favour the large $$ regime implying that the environment-dependent dilaton satisfies two of the swampland conjectures, i.e. the distance conjecture whereby the field excursion should not exceed the Planck scale and the de Sitter conjecture specifying that the running dilaton potential should be steep enough with a large $$ .