@misc{CaprasseDemaretGatermannetal., author = {Caprasse, H. and Demaret, J. and Gatermann, Karin and Melenk, Herbert}, title = {Power-Law Type Solutions of Fourth-Order Gravity}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-466}, number = {SC-90-18}, abstract = {We study the power-law type solutions of the fourth order field equations derived from a generic quadratic Lagrangian density in the case of multidimensional Bianchi I cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the Groebner bases associated to it. While, in space dimension \$ d = 3 \$ , the Einsteinian Kasner metric is still the most general power-law type solution, for \$ d > 3 \$ , no solution, other than the Minkowski space-time, is common to the three systems of equations associated with the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the \$ d \$-dimensional space into a ( \$ d - 3 \$)-dimensional internal space and a physical 3- dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when \$ d = 9 \$).}, language = {en} }