Examining Non-Linearities with Screened Fifth Forces - Thrussell, Ben (2021)
Alternative theories of gravity often feature new degrees of freedom in addition to those of the metric tensor that are present in general relativity. One such class of alternative gravitational theories are scalar--tensor theories, which generally predict the existence of a `fifth force' mediated by a scalar field through a non-minimal coupling to gravity. Such forces are constrained both by laboratory experiments and by observations of our solar system, but `screening' mechanisms weaken these constraints by suppressing the fifth force in the presence of a high matter density, allowing the dynamics of the scalar field to be relevant on cosmological scales but invisible to our most sensitive experiments. Nevertheless, many experimental and observational methods for testing screened fifth forces have been proposed. To fully understand their prospects for detecting or constraining new scalar fields, one must ensure that the behaviour of these fields is accurately represented by any approximations that are made in the process of calculating observables. Contributions to this behaviour may include non-linearities in the scalar field's bare potential, the non-minimal coupling between the field and its own stress--energy, and quantum corrections. This thesis will study all three of these effects, both in isolation and in the context of two important scenarios, for two types of screening: the symmetron, in which the strength of the scalar field's coupling to matter varies with the background matter density, and the chameleon, in which it is the Compton wavelength of the scalar field that varies. The first scenario is black hole superradiance, an astrophysical phenomenon that can be used to probe any bosonic field through the universality of the gravitational interaction. It will be shown that non-linearities are important for screened scalar fields undergoing a superradiant instability, but that previous studies on axion-like particles are not entirely relevant for symmetrons and chameleons; namely, no `bosenova' is expected to occur for these models. The second scenario is that of static field profiles around spherical and cylindrical sources, with particular focus being on the limit in which these sources are point-like compared to the field's Compton wavelength. Scaling relationships for the field profiles are obtained, and screening factors are calculated which show that the symmetron model is well approximated by conventional analytical approximations, while a similar chameleon model requires numerical methods to obtain accurate results.