Abstract
Many non-linear scalar field theories possess a screening mechanism that can suppress any associated fifth force in dense environments. As a result, these theories can evade local experimental tests of new forces. Chameleon-like screening, which occurs because of non-linearities in the scalar potential or the coupling to matter, is well understood around extended objects. However, many experimental tests of these theories involve objects with spatial extent much smaller than the scalar field's Compton wavelength, and which could therefore be considered point-like. In this work, we determine how the fifth forces are screened in the limit that the source objects become extremely compact.
Highlights
Many non-linear scalar field theories possess a screening mechanism that can suppress any associated fifth force in dense environments
The two key benchmark models relevant to this paper are the chameleon model [14,15,16], which relies on non-linearities in the potential to make fluctuations more massive in dense environments, and the symmetron model [17, 18], which instead relies on a non-linear potential and a quadratic coupling to matter to vary both the mass of the field and the strength of the coupling to matter depending on the local energy density
The aim of this work was to study the screening of fifth forces around extremely compact sources that are effectively point-like compared to the Compton wavelength of the scalar fifth-force mediator
Summary
We introduce the scalar-tensor theories that will be the focus of this article. The fifth forces that the additional scalar fields mediate are subject to screening mechanisms, which arise due to non-linear terms in their “effective potentials”.2. Since we will focus on solutions in Minkowski spacetime, we have chosen to work in the so-called Einstein frame, wherein the gravitational part of the action has a canonical Einstein-Hilbert form, and the canonically normalised scalar field φ is coupled directly to the trace of the matter energy-momentum tensor. Making the minimal assumption of a single mass scale M and restricting ourselves to the regime φ/M 1, we can expand the coupling function as a power series in φ/M This series will yield non-renormalisable operators, and we have an effective field theory with a cut-off scale parametrically related to M. To the coupling as it appears in the effective potential, not as it appears in the equation of motion
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