A renormalization group method for studying the early universe in the Lorentzian IIB matrix model

Abstract

We propose a new method for studying the early universe in the Lorentzian version of the IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. This method is based on the idea of renormalization group, and it enables us to study the time-evolution of the universe for much longer time than in the previous work, which showed that the SO(9) rotational symmetry is spontaneously broken down to SO(3) after a "critical time". We demonstrate how this method works in a simplified model, which is expected to capture the behaviors of the original model when the space is not so large. In particular, we present clear evidence that the three-dimensional space expands exponentially after the critical time in this simplified model.

21 pages, 16 figures, (v2) references added, typos corrected, (v3) Appendix added

References in corpus (6)

• Symmetry, Gravity and Noncommutativity
• Emergent Gravity from Noncommutative Spacetime
• Cosmological solutions of emergent noncommutative gravity
• Matrix String Description of Cosmic Singularities in a Class of Time-dependent Solutions
• Higher Order Terms of Improved Mean Field Approximation for IIB Matrix Model and Emergence of Four-dimensional Space-time
• Spontaneous breaking of the rotational symmetry in dimensionally reduced super Yang-Mills models

Cited by in corpus (9)

• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Emergent Cosmology from Matrix Theory
• Matrix Model Approach to Cosmology
• Progress in the numerical studies of the type IIB matrix model
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• Fuzzy $C{P}^2$ Space-Times
• A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model