Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Abstract

We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions are obtained, depending on the mass parameters.Comment: 22 pages, 4 figures. V2,V3: improved discussion, typos fixed. V3: published versio