Lattice Refining Loop Quantum Cosmology and Inflation

TL;DR

This paper investigates how lattice refinement in loop quantum cosmology influences the viability of inflation, showing that refinement is essential for natural inflation models consistent with observational data.

Contribution

It demonstrates that lattice refinement is crucial for achieving natural inflation in loop quantum cosmology, providing constraints on the inflationary potential and scalar field parameters.

Findings

Lattice refinement is necessary for successful inflation models.

Fixed lattice models require fine-tuning of parameters.

Refinement models align better with observational constraints.

Abstract

We study the importance of lattice refinement in achieving a successful inflationary era. We solve, in the continuum limit, the second order difference equation governing the quantum evolution in loop quantun cosmology, assuming both a fixed and a dynamically varying lattice in a suitable refinement model. We thus impose a constraint on the potential of a scalar field, so that the continuum approximation is not broken. Considering that such a scalar field could play the role of the inflaton, we obtain a second constraint on the inflationary potential so that there is consistency with the CMB data on large angular scales. For a $m^2\phi^2/2$ inflationary model, we combine the two constraints on the inflaton potential to impose an upper limit on $m$, which is severely fine-tuned in the case of a fixed lattice. We thus conclude that lattice refinement is necessary to achieve a natural inflationary model.