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I will discuss a solution generating technique that allows to generate stationary axisymmetric solutions of five-dimensional gravity, starting from static ones. This technique can be used to add angular momentum to static configurations. It can also be used to add KK-monopole charge to asymptotically flat five-dimensional solutions, thus generating geometries that interpolate between five-dimensional and four-dimensional solutions.

The k-essence theories admit the superluminal propagation of the perturbations on classical nontrivial backgrounds. In this talk I will review our arguments from arXiv:0708.0561v1 and show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity.

We investigate the effect of evaporating primordial black holes on the ionization history of the universe, with emphasis on limits derivable from the CMB and future 21-cm observations of high-redshift neutral hydrogen.

The cosmological power of Type Ia Supernovae depends on their ability to determine distances. The astrophysical limitations, like reddening, local velocity inhomogeneities and intrinsic variations, are a severe impediment for the cosmological applications of these cosmic explosions. Overcoming these systematic restrictions must be the goal of any future supernova projects.