Year: 2007
Type: article
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 quantum 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 cosmic microwave background data on large angular scales. For a ${m}^{2}{\ensuremath{\phi}}^{2}/2$ 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.
Authors: William Nelson, Mairi Sakellariadou
Institution: King's College London
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
OpenAlex ID: W2127601629