Polymerized spacetime dynamics with multi-field source: unraveling the pre-inflationary Universe

TL;DR

This paper explores a multi-field Loop Quantum Cosmology model with polymerization, revealing quantum bounce, transition, and inflation phases, and analyzing their stability and observational viability.

Contribution

It introduces a Hamiltonian formulation with geometric couplings for multi-field models and applies polymerization to derive quantum-corrected cosmological dynamics.

Findings

Quantum bounce replaces classical singularity.

Successful slow-roll inflation with sufficient e-folds.

Stable background evolution under certain initial conditions.

Abstract

We study a multi-field model in Loop Quantum Cosmology for a maximally symmetric spacetime governed by the Einstein--Hilbert action minimally coupled to scalar fields. Using a Legendre transformation, we formulate the Hamiltonian dynamics in canonically equivalent geometrodynamical and Yang--Mills--type representations, incorporating nontrivial couplings through a geometric structure on the multi-field configuration space. Implementing the $\bar{\mu}$-scheme polymerization, we obtain the loop-quantum-corrected Friedmann equations. By focusing on the two-field model as an example, we analyze the effective dynamics for specific potentials. The \textit{quantum bouncing, transition, and slow-roll inflationary} phases are investigated numerically, and viability of the models is assessed by evaluating the number of e-folds during the inflationary phase for certain given initial conditions. The global behavior of the background evolution is further examined through linear stability and dynamical-systems analyses.