Planck-scale structure of spacetime and some implications for astrophysics and cosmology

Abstract

I briefly review some scenarios for the role of the Planck length in quantum gravity. In particular, I examine the differences between the schemes in which quantum gravity is expected to introduce a maximum acceleration and the schemes in which the Planck length sets the minimum value of wavelengths (maximum value of momentum). I also comment on some pictures for the structure of spacetime at the Planck scale, such as spacetime discretization and spacetime noncommutativity. I stress that some of these proposals can have significant implications in astrophysics and cosmology.Comment: 9 pages, LaTex. Invited talk at ``Thinking, Observing and Mining the Universe", Sorrento, Italy, September 22-27, 2003 (to appear in the proceedings). V2: Paper unchanged, some references adde