Brane-world cosmology in higher derivative gravity or warped compactification in the next-to-leading order of AdS/CFT correspondence

The general model of higher-derivative (HD) gravity is considered. The sear ch of brane-world cosmology in such theory is presented when bulk is d5 AdS and boundary is spherical, hyperbolic or at (single) brane. It is found th e wide range of theory parameters where such cosmology may be realized. Spe cial attention is paid to the version of HD theory representing SG dual of N = 2 Sp(N) SCFT (in next-to-leading order of large-N expansion). In partic ular, it is shown that inflationary brane Universe does not occur for SG du al while hyperbolic brane occurs (which was not possible in leading order). The quantum effects of CFT living on the brane (via the corresponding conf ormal anomaly induced effective action) may qualitatively change the result s of classical analysis. There appears inflationary (or hyperbolic) brane U niverse induced by only quantum effects. In AdS/CFT correspondence (next-to -leading order) the addition of such CFT effective action (in some energy r egion) is naturally explained in terms of holographic renormalization group . It results in the possibility of quantum creation of inflationary brane U niverse (with small rate) even for SG dual.