Effective scalar-tensor description of regularized Lovelock gravity in four dimensions

We reformulate the recently proposed regularized version of Lovelock gravity in four dimensions as a scalar-tensor theory. By promoting the warp factor of the internal space to a scalar degree of freedom by means of Kaluza-Klein reduction, we show that regularized Lovelock gravity can be described effectively by a certain subclass of the Horndeski theory. Cosmological aspects of this particular scalar-tensor theory are studied. It is found that the background with a scalar charge is generically allowed. The consequences of this scalar charge are briefly discussed.