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arXiv · 0706.0179

Lattice Refining Loop Quantum Cosmology and Inflation

William Nelson·Mairi Sakellariadou
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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 $m^2ϕ^2/2$ 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.

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William Nelson, Mairi Sakellariadou. 2007-06-30. Lattice Refining Loop Quantum Cosmology and Inflation. https://doi.org/10.1103/physrevd.76.044015

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