Quantum Gravity and Inflation

TL;DR

This paper develops exact quantum cosmology solutions using loop quantum gravity variables, modeling inflating universes with a scalar field as time, revealing an attractor behavior and addressing the normalizability of the Kodama state.

Contribution

It introduces a new class of exact solutions in quantum cosmology with scalar fields, extending the Kodama state and analyzing inflationary attractors within loop quantum gravity.

Findings

Exact solutions for inflating universes in quantum cosmology.

Evidence of an attractor indicating universality in inflation.

Resolution of the Kodama state's normalizability issue.

Abstract

Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field, that corresponds to inflating universes. The scalar field, which has an arbitrary potential, is treated as a time variable, reducing the hamiltonian constraint to a time-dependent Schroedinger equation. When reduced to the homogeneous and isotropic case, this is solved exactly by a set of solutions that extend the Kodama state, taking into account the time dependence of the vacuum energy. Each quantum state corresponds to a classical solution of the Hamiltonian-Jacobi equation. The study of the latter shows evidence for an attractor, suggesting a universality in the phenomena of inflation. Finally, wavepackets can be constructed by superposing solutions with different ratios of kinetic to potential scalar field energy, resolving, at least in this case, the issue of normalizability of the Kodama state.