Inflationary scalar spectrum in loop quantum cosmology

Abstract

In the context of loop quantum cosmology, we consider an inflationary era driven by a canonical scalar field and occurring in the semiclassical regime, where spacetime is a continuum but quantum gravitational effects are important. The spectral amplitude and index of scalar perturbations on an unperturbed de Sitter background are computed at lowest order in the slow-roll parameters. The scalar spectrum can be blue-tilted and far from scale invariance, and tuning of the quantization ambiguities is necessary for agreement with observations. The results are extended to a generalized quantization scheme including those proposed in the literature. Quantization of the matter field at sub-horizon scales can provide a consistency check of such schemes.

29 pages, 2 figures. v2: typos corrected, discussion improved and extended, new section added. Conclusions are unchanged

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• The gravitational wave background from super-inflation in Loop Quantum Cosmology
• Thermal fluctuations in loop cosmology
• Relic gravitons as the observable for Loop Quantum Cosmology