Dynamically generated four-dimensional models in Lovelock cosmology

Abstract

We consider a class of $D$-dimensional Lovelock models provided with a positive cosmological constant whose induced metric is given by the product of the metrics of a three-dimensional (external) and a $D\ensuremath{-}4$-dimensional (internal) maximally symmetric space. When all the Lovelock coefficients are non-negative, we show that these models admit classical solutions with a constant internal scale factor, and that for these solutions the evolution of the external dimensions can be described by a four-dimensional Einstein theory with a positive effective Hilbert-Einstein coefficient and non-negative effective cosmological constant. In addition, we prove that the perturbative formalism for the treatment of the Lovelock model is always well defined in the region of the gravitational configuration space covered by the considered solutions with a constant internal scale factor. We also examine the dynamically generated four-dimensional theory that is obtained when the internal scale factor remains constant, and discuss the role played by the no-boundary condition in the corresponding process of reducing the degrees of freedom of the minisuperspace model.