In this paper we propose a scheme which allows one to find all possibleexponential solutions of special class -- non-constant volume solutions -- inLovelock gravity in arbitrary number of dimensions and with arbitratecombinations of Lovelock terms. We apply this scheme to (6+1)- and(7+1)-dimensional flat anisotropic cosmologies in Einstein-Gauss-Bonnet andthird-order Lovelock gravity to demonstrate how our scheme does work. In courseof this demonstration we derive all possible solutions in (6+1) and (7+1)dimensions and compare solutions and their abundance between cases withdifferent Lovelock terms present. As a special but more "physical" case weconsider spaces which allow three-dimensional isotropic subspace for they couldbe viewed as examples of compactification schemes. Our results suggest that thesame solution with three-dimensional isotropic subspace is more "probable" tooccur in the model with most possible Lovelock terms taken into account, whichcould be used as kind of anthropic argument for consideration of Lovelock andother higher-order gravity models in multidimensional cosmologies.
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