A Matrix Model for Misner Universe and Closed String Tachyons

Abstract

We use D-instantons to probe the geometry of Misner universe, and calculate the world volume field theory action, which is of the 1+0 dimensional form and highly non-local. Turning on closed string tachyons, we see from the deformed moduli space of the D-instantons that the spacelike singularity is removed and the region near the singularity becomes a fuzzy cone, where space and time do not commute. When realized cosmologically there can be controllable trans-planckian effects. And the infinite past is now causally connected with the infinite future, thus also providing a model for big crunch/big bang transition. In the spirit of IKKT matrix theory, we propose that the D-instanton action here provides a holographic description for Misner universe and time is generated dynamically. In addition we show that winding string production from the vacua and instability of D-branes have simple uniform interpretations in this second quantized formalism.

15 pages, no figures, harvmac; added discussion on space-time noncommutativity and consequences in cosmology; some conclusions better clarified, added comparison with McGreevy & Silverstein's work, added footnotes and references

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• Towards A Nonsingular Tachyonic Big Crunch
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