Algebraic connections on parallel universes

For any manifold $M$, we introduce a \ZZ -graded differential algebra $\Xi$, which, in particular, is a bi-module over the associative algebra $C(M\cup M)$. We then introduce the corresponding covariant differentials and show how this construction can be interpreted in terms of Yang-Mills and Higgs fields. This is a particular example of noncommutative geometry. It differs from the prescription of Connes in the following way: The definition of $\Xi$ does not rely on a given Dirac-Yukawa operator acting on a space of spinors.Comment: 10 pages, CPT-93/PE 294

Dark/Visible Parallel Universes and Big Bang Nucleosynthesis

We develop a model for visible matter-dark matter interaction based on the exchange of a massive gray boson called herein the Mulato. Our model hinges on the assumption that all known particles in the visible matter have their counterparts in the dark matter. We postulate six families of particles five of which are dark. This leads to the unavoidable postulation of six parallel worlds, the visible one and five invisible worlds. A close study of big bang nucleosynthesis (BBN), baryon asymmetries, cosmic microwave background (CMB) bounds, galaxy dynamics, together with the Standard Model assumptions, help us to set a limit on the mass and width of the new gauge boson. Modification of the statistics underlying the kinetic energy distribution of particles during the BBN is also discussed. The changes in reaction rates during the BBN due to a departure from the Debye-Hueckel electron screening model is also investigated.Comment: Invited talk at the Workshops "CompStar: the physics and astrophysics of compact stars", Tahiti, June 4-8, 2012, "New Directions in Nuclear Astrophysics", Castiglion Fiorentino, Italy, June 18-22, 2012, and "Carpathian Summer School of Physics", Sinaia, Romania, June 24 - July 7, 2012. To be published in AIP Proceeding