Lattice loop quantum cosmology: scalar perturbations

Abstract

We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques. The appropriate interactions between nearby cells are included in the Hamiltonian in order to obtain the correct physics. It is shown that the quantum theory is anomaly-free: the scalar and diffeomorphism constraint operators weakly commute with the Hamiltonian. Finally, the effective theory encoding the leading order quantum gravity corrections is derived and is shown to give the same holonomy-corrected effective equations that have been obtained in previous studies.

32 pages, v2: Minor changes

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• Bouncing cosmologies with dark matter and dark energy
• An Extended Matter Bounce Scenario: current status and challenges
• A $\Lambda$CDM bounce scenario
• On the fate of quantum black holes
• Testing loop quantum cosmology
• Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics
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• The separate universe framework in group field theory condensate cosmology
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• Separate universes in loop quantum cosmology: framework and applications
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• Some conceptual issues in loop quantum cosmology
• Scalar spectra of primordial perturbations in loop quantum cosmology
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• Loop Quantum Cosmology
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• Inflationary power spectra with quantum holonomy corrections
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• Semiclassical solutions of generalized Wheeler-DeWitt cosmology
• Tachyon warm inflation with the effects of Loop Quantum Cosmology in the light of Planck 2015
• Running of the Spectral index in Deformed Matter Bounce Scenarios with Hubble-rate-dependent Dark Energy
• The Physical Relevance of the Fiducial Cell in Loop Quantum Cosmology
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC