Loop quantum cosmology with higher order holonomy corrections

TL;DR

This paper rigorously formulates loop quantum cosmology with higher order holonomy corrections, showing that the quantum bounce persists and matter density remains finite, highlighting the intrinsic discreteness of LQC and its difference from WDW theory.

Contribution

It extends the quantum theory of LQC to include higher order holonomy corrections and demonstrates the robustness of the quantum bounce across all correction orders.

Findings

Matter density is bounded above by a critical density.

Quantum bounce connects expanding and contracting solutions.

Higher order corrections can be interpreted via SU(2) representations.

Abstract

With a well-motivated extension of higher order holonomy corrections, the quantum theory of loop quantum cosmology (LQC) for the $k=0$ Friedmann-Robertson-Walker model (with a free massless scalar) is rigorously formulated. The analytical investigation reveals that, regardless of the order of holonomy corrections and for any arbitrary states, the matter density remains finite, bounded from above by an upper bound, which equals the critical density obtained at the level of heuristic effective dynamics. Particularly, with all orders of corrections included, the dynamical evolution is shown to follow the bouncing scenario in which two Wheeler-DeWitt (WDW) solutions (expanding and contracting) are bridged together through the quantum bounce. These observations provide further evidence that the quantum bounce is essentially a consequence of the intrinsic discreteness of LQC and LQC is fundamentally different from the WDW theory. Meanwhile, the possibility is also explored that the higher order holonomy corrections can be interpreted as a result of admitting generic SU(2) representations for the Hamiltonian constraint operators.