Towards Cosmological Dynamics from Loop Quantum Gravity

TL;DR

This paper investigates cosmological dynamics derived from an effective Hamiltonian in loop quantum gravity, revealing non-singular bounces, asymmetric bounce behavior, and conditions for inflation consistent with observations.

Contribution

It provides a systematic analysis of cosmological dynamics from a Hamiltonian in loop quantum gravity, highlighting higher-order corrections and the nature of the bounce.

Findings

Quantum geometric effects cause non-singular, asymmetric bounces.

Pre-bounce universe approaches de Sitter space, post-bounce recovers classical GR.

Slow-roll inflation naturally occurs after the bounce.

Abstract

We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC causing a non-singular bounce. Dynamics can be described by the Hamilton's or the Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one-to-one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the pre-bounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the post-bounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.