Spacetime Emergence in the Robertson-Walker Universe from a Matrix model

Abstract

Using a novel, string theory-inspired formalism based on a Hamiltonian constraint, we obtain a conformal mechanical system for the spatially flat four-dimensional Robertson-Walker Universe. Depending on parameter choices, this system describes either a relativistic particle in the Robertson-Walker background, or metric fluctuations of the Robertson-Walker geometry. Moreover we derive a tree-level M-theory matrix model in this time-dependent background. Imposing the Hamiltonian constraint forces the spacetime geometry to be fuzzy near the big bang, while the classical Robertson-Walker geometry emerges as the Universe expands. From our approach we also derive the temperature of the Universe interpolating between the radiation and matter dominated eras.

4 pages - accepted for publication in Physical Review Letters

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• Matrix Model Approach to Cosmology
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• A renormalization procedure for tensor models and scalar-tensor theories of gravity
• Einstein's Field Equations as a Fold Bifurcation
• Inflation with a stringy minimal length, reworked
• Conformal structure of FLRW Cosmology: Spinorial representation and the so(3,2) algebra of observables
• Analogue spacetimes: Toy models for "quantum gravity''