Classical and quantum Lovelock cosmology

In this work we consider a $D$-dimensional ($D\ge 3$) homogeneous and isotropic minisuperspace model provided with a Lovelock Lagrangian. We introduce a procedure by which we associate to the system a unique classical solution. For very weak conditions on the Lovelock coefficients and at least for positive Lorentzian energy densities we show that this solution is uniquely determined by the rather natural physical requirement that the Euclidean solution is flat when we add no matter to the system. In these cases, the given classical solution can be interpreted in terms of perturbations to the corresponding Einstein solution. We also discuss the associated Wheeler-DeWitt equation and apply our results to the model with a cosmological constant and a massive scalar field model.