f(R) theories and Gauge Theory Gravity

Anthony Lasenby, Cavendish Astrophysics Group, UK

We consider a `Gauge Theory of Gravity' approach to f(R) theories. These theories, where the gravitational part of the Lagrangian is generalised to a general function, f(R) of the Ricci scalar, have over recent years become very popular as possible theories of modified gravity, and have been applied to explanations of both Dark Energy and Dark Matter. Two different variants exist, one based on a purely metric approach, and the other, `Palatini f(R) theory', where the equations are derived via treating the connection as an independent entity, and there has been considerable discussion over which of these approaches should be adopted, and which, if either, is compatible with the observations. In Gauge Theory Gravity, which is based on the Geometric Algebra of spacetime, relativistic gravity is treated as much as possible as a gauge theory like others, and the independent variables are derived from local symmetry principles. This means the route through to the equations of motion is fixed once the Lagrangian is specified, and one can be certain what the conclusions of the theory are for a given Lagrangian. We apply this approach to f(R) theories and find that Palatini-type variational equations are favoured, although with torsion being inevitable as well. However, the torsion is found to be of a type that does not directly affect the equations of motion for particles and fields, entering only via its indirect effects on the metric. A particular popular choice of f(R) aimed at giving late-time acceleration of the Universe is then investigated, and it is found that while it succeeds in its cosmological purpose, it has surprising effects both on the dark energy equation of state and the rotation curves of galaxies.