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We study some aspects of cosmologies in 5D models with one infinite extra dimension. Matter is confined to the brane, gravity extends to the bulk. Models with positive and negative tension of the brane are considered. Cosmological evolution of the 4D world is described by warped solutions of the generalized Friedmann equation. Cosmological solutions on the brane are obtained with the input of the present-time observational cosmological parameters. We estimate the age of the Universe and abundance of 4 He produced in primordial nucleosynthesis in different models. Using these estimates we find constraints on dimensionless combinations of the 5D gravitational scale, scale of the warp factor and coupling at the 4D curvature term in the action.

Near-horizon symmetries are studied for black hole solutions to Einstein equations containing supertranslation field constructed by Compere and Long. The metric is transformed to variables in which the horizon is located at the surface r = 2M , where M is the mass of black hole. We consider general diffeomorphisms which preserve the gauge and the near-horizon structure of the metric and find the corresponding transformations of metric components. We review the action of the generators of supertranslations preserving the static gauge of the metric and determine a subgroup of supertranslations preserving the gauge and near-horizon structure of the metric. Variation of the surface charge corresponding to the Killing vectors of asymptotic horizon symmetries is calculated. Sufficient conditions of integrability of the variation of the surface charge to a closed integral form are found and an example of metrics with integrable charge variation is discussed.

Within the framework of "anomalously gauged" Wess–Zumino–Witten (WZW) models, we construct solutions which include non-Abelian fields. Both compact and noncompact groups are discussed. In the case of compact groups, as an example of background containing non-Abelian fields, we discuss conformal theory on the SO(4)/SO(3) coset, which is the natural generalization of the 2-D monopole theory corresponding to the SO(3)/SO(2) coset. In noncompact case, we consider examples with SO(2, 1)/SO(1, 1) and SO(3, 2)/SO(3, 1) cosets.