Braneworlds in bimetric theories

Full text: The brane theory has been investigated as a candidate for solving the hierarchy problem, and other problems in high energy physics. In the Randall-Sundrum model, we can add scalar fields with usual dynamics and allow them to interact with gravity in the standard way. The study of scalar fields coupled to gravity in warped geometries has been frequently reported in the literature, and in the current work we consider a model driven by a single real scalar field. We investigate the presence of braneworld solutions in a bimetric theory, with gravity and the scalar field coupling differently. We consider a non-standard model, with a Cuscuton-like scalar field, and we show how to generate braneworld solutions in this new scenario. In particular, we found no gravitational instabilities for the braneworld solutions. We consider that the non-standard kinetic term arises due to the coupling with a different metric used to describe the gravitational field, that is, we use a bimetric theory. Bimetric theories have been proposed as VSL (varying speed of light) theories, motivated to solve the horizon, flatness, and dark matter problems. In the model, there are two metrics: g_μν (which we refer to as the gravitational metric) which is used to construct the Einstein-Hilbert action; and ĝg_μν (which we refer to as the matter metric), used to construct the matter action via minimal coupling, providing the geometry on which matter fields propagate and interact. Despite the simple structure of the equations of motion (in the case of a purely unconventional kinetic term), such as the absence of second derivatives, we see that the model can describe brane solutions with a very simple potential. However, in this context, transformation connecting the two metrics has an additional term that comes from a vector normal to the brane. This term allows to change dynamics in bimetric theory, such as DBI-like to Cuscuton dynamics. (author)