Perturbative formalism of Lovelock gravity

In this work we develop a perturbative formalism for the treatment of Lovelock theories of gravity. We consider in detail D-dimensional models in Lovelock gravity with an induced metric given by the product of the metrics of two maximally symmetric spaces. We first explicitly obtain the Lovelock action, Hamiltonian constraint, gravitational momenta, and dynamical equations for this type of minisuperspace model. We then apply the perturbative formalism and show how it solves the partial degeneration and multivaluedness problems in the analyzed Lovelock models. We also study the implementation of the proposed perturbative formalism in models whose induced metric is a product of metrics of an arbitrary number of maximally symmetric spaces. We finally comment on the generalization of this formalism to Lovelock gravity in superspace.