Abstract
Abstract We present evidence that recent numerical results from the reduced classical equations of the Lorentzian IIB matrix model can be interpreted as corresponding to the emergence of an expanding universe. In addition, we propose an effective metric to describe the emerging (3+1)D spacetime. This metric gives, at all times, finite values for the Ricci and Kretschmann curvature scalars. With these results, we are able to give a heuristic discussion of the origin of the Universe in the context of the IIB matrix model.
Highlights
The Ishibashi–Kawai–Kitazawa–Tsuchiya (IKKT) large-N matrix model [1] has been proposed as a nonperturbative definition of (9+1)D type-IIB superstring theory
Numerical investigations [3,4] of the Lorentzian version of the IKKT matrix model have found indications that three spatial dimensions emerge which behave differently from the remaining six spatial dimensions and that the “late-time” behavior of these three spatial dimensions may be controlled by a classical configuration of the matrices
Further numerical results have been presented [5] from the matrix-model classical equations with a particular Ansatz for the ten bosonic matrices, where the Ansatz implements the split of a (3+1)D “spacetime” and a 6D “internal space.”
Summary
The Ishibashi–Kawai–Kitazawa–Tsuchiya (IKKT) large-N matrix model [1] has been proposed as a nonperturbative definition of (9+1)D type-IIB superstring theory. In the bottom-left panel of Fig. 1, the apparently increasing gap near zero for larger and larger values of |t| just appears because a larger and larger interval is covered by a fixed number (n) of points Both issues will be discussed further below. The square of the cosmic scale factor a(t) in the metric (7) can be identified with the quantity R 2(t) obtained from the classical results of the large-N matrix model It is, namely, not at all clear that the genuine Lorentzian large-N matrix model [1,2,3,4], and not just the set of corresponding classical equations [5], gives a nonsingular bouncing cosmology as suggested by Fig. 3 of Ref.
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