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A Model of Spacetime Emergence in the Early Universe

  • Author(s): Tysanner, Martin William
  • Advisor(s): Aguirre, Anthony
  • et al.

This thesis proposes and develops much of the groundwork for a model of emergent physics, posited to describe the initial condition and early evolution of a universe. Two different considerations motivate the model. First, the spacetime manifold underlying general relativity and quantum theory is a complex object with much structure, but its origin is unexplained by the standard picture. Second, it is argued, the usual assumption of the preexistence of this manifold leads to possibly intractable theoretical (not observational) difficulties with the usual cosmological inflation idea. Consistent with both considerations, the assumption of a manifold that precedes a big bang cosmology is dropped; instead, a spacetime manifold with metric, Lorentz symmetry, and manifestation of standard quantum fields propagating on the spacetime all emerge in the model from a simpler, statistically scale invariant underlying structure, driven by an inflation-like process.

The basic structural components of the model are a stochastic (not quantum or classical) scalar field on a general metric space, plus a collection of quantum fields that supply the matter content once spacetime begins to emerge. Importantly, standard quantum fields cannot be defined on the pre-emergent space; this is addressed by assuming quantum theory exists a priori, and then postulating that quantum fields can begin to manifest once an approximate spacetime has emerged. Atypical fluctuations in the scalar field transiently break the statistical scale invariance in a localized region of the general metric space; a very small subset have field configurations of approximate spacetimes which can potentially evolve into an initial condition for a universe. Spacetime structure and geometry then arise from the dependence of propagation speeds and spatial/temporal distances on variations in the scalar field; these variations are seeded by the matter (quantum) fields.

The thesis develops the mathematics of the basic components of the model in some detail, outlines a mechanism whereby scale invariance is broken and dimensionality is fixed, and develops processes and scenarios wherein variations in the scalar field can lead to spacetime geometry in an inflation-like process. The resulting picture of spacetime is then compared with that of general relativity.

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