Some notes on the Big Trip

The big trip is a cosmological process thought to occur in the future by which the entire universe would be engulfed inside a gigantic wormhole and might travel through it along space and time. In this paper we discuss different arguments that have been raised against the viability of that process, reaching the conclusions that the process can actually occur by accretion of phantom energy onto the wormholes and that it is stable and might occur in the global context of a multiverse model. We finally argue that the big trip does not contradict any holographic bounds on entropy and information.Comment: 8 pages, no figures, LaTe

Dark energy without dark energy

It is proposed that the current acceleration of the universe is not originated by the existence of a mysterious dark energy fluid nor by the action of extra terms in the gravity Lagrangian, but just from the sub-quantum potential associated with the CMB particles. The resulting cosmic scenario corresponds to a benigner phantom model which is free from the main problems of the current phantom approaches.Comment: 4 pages, 1 figure, to appear in AIP proceedings of "Dark side of the Universe

Toric embedded resolutions of quasi-ordinary hypersurface singularities

We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485-503. In the first procedure the singularity is embedded as hypersurface. In the second procedure, which is inspired by a work of Goldin and Teissier for plane curves (see Resolving singularities of plane analytic branches with one toric morphism,loc. cit., pages 315-340), we re-embed the singularity in an affine space of bigger dimension in such a way that one toric morphism provides its embedded resolution. We compare both procedures and we show that they coincide under suitable hypothesis.Comment: To apear in Annales de l'Institut Fourier (Grenoble