Can non-commutativity resolve the big-bang singularity?
Laboratoire de Physique Théorique, Université de Paris-Sud, Bâtiment 211, 91405, Orsay, France
2 Department of Engineering Sciences, University of Patras, 26110, Patras, Greece
3 Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens, Greece
4 Theory Division, CERN, 1211, Geneva 23, Switzerland
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A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized.
© Springer-Verlag, 2004