Polymerized spacetime dynamics with multifield source: Unraveling the pre-inflationary Universe

Abstract

We study a multifield 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 multifield configuration space. Implementing the $\bar{\mu }$-scheme polymerization, we obtain the loop-quantum-corrected Friedmann equations. By focusing on the two-field models 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.

20 pages, 10 figures, 8 tables, Replaced with the version matching the published one in the Phys. Rev. D