Lovelock gravity is equivalent to Einstein gravity coupled to form fields

Lovelock gravity is a class of higher-derivative gravitational theories for which the linearized equations of motion have no more than two time derivatives. Here, it is shown that any Lovelock theory can be effectively described as Einstein gravity coupled to a p-form gauge field. This extends the known example of an $f(R)$ theory of gravity, which can be described as Einstein gravity coupled to a scalar field.