Quantum Nature of the Big Bang

TL;DR

The known results on the resolution of the big-bang singularity in loop quantum cosmology are significantly extended, and unlike in other approaches the quantum evolution is deterministic across the deep Planck regime.

Abstract

Some long standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big bang singularity in loop quantum cosmology are significantly extended as follows: 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.

Figures (2)

• Figure 1: The absolute value of the wave function $\Psi$ is plotted as a function of $\phi$ and $\mu$ (whose values are shown in multiples of $\mu_o$). For visualization clarity, only the values of $|\Psi|$ greater than $10^{-4}$ are shown. Being a physical state, $\Psi$ is symmetric under $\mu \rightarrow -\mu$.
• Figure 2: The expectation values of Dirac observables $\hat{\mu}|_{\phi}$ are plotted (in multiples of $\mu_o$), together with their dispersions. They exhibit a quantum bounce which joins the contracting and expanding classical trajectories marked by fainter lines.