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

TL;DR

This paper introduces a string theory-inspired formalism that models the emergence of classical spacetime geometry from a matrix model in a Robertson-Walker universe, capturing early universe fuzziness and later classical expansion.

Contribution

It develops a novel Hamiltonian constraint-based formalism linking matrix models to spacetime emergence in cosmology, including a derivation of the universe's temperature evolution.

Findings

Spacetime becomes fuzzy near the big bang due to Hamiltonian constraints.

Classical Robertson-Walker geometry emerges as the universe expands.

Derived the temperature evolution from radiation to matter domination eras.

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.