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.
Highlights
A good picture of branes arising as classical solutions, with IIB supergravity interactions arising at the loop level [1,2,3,4]
The Big Bang (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 BB arises from a signature change in the effective metric, taking into account the quantized 4-volume form which arises from the non-commutative structure of the brane
Summary
We are interested in solutions of the following IKKT-type matrix model [1] with mass terms. We will study solutions of these equations which are interpreted as 3+1-dimensional space-times, as noncommutative “branes“ embedded in target space. SUSY is broken spontaneously and softly, but we expect that this still ensures sufficient UV cancellations to tame the quantum corrections These mass terms are important because they introduce a scale into the model, and quantum corrections are expected to induce such mass terms on curved backgrounds. Since we only study classical solutions of (2.2) and their geometrical properties, we will restrict ourselves to the bosonic part of (2.1), including the mass terms by hand. There are no finite-dimensional non-trivial solutions without a mass term, as shown in the appendix
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