Quantum Nature of the Big Bang: An Analytical and Numerical Investigation

TL;DR

This paper develops analytical and numerical methods in loop quantum cosmology to demonstrate that the big bang singularity is replaced by a quantum bounce, with a detailed framework for understanding quantum effects in early universe models.

Contribution

It introduces rigorous constructions of the physical Hilbert space, Dirac observables, and semi-classical states, extending the analysis of quantum geometry effects in cosmology.

Findings

The scalar field acts as an internal clock, realizing emergent time.

The big bang is replaced by a deterministic quantum bounce.

The methods provide a foundation for analyzing more general models.

Abstract

Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors and significantly extend the known results on the resolution of the big bang singularity. Specifically, the following results are established for the homogeneous isotropic model with a massless scalar field: i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac observables and semi-classical states are constructed rigorously; iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the non-perturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime. Our constructions also provide a conceptual framework and technical tools which can be used in more general models. In this sense, they provide foundations for analyzing physical issues associated with the Planck regime of loop quantum cosmology as a whole.