Primordial tensor modes of the early Universe

Abstract

We study cosmological tensor perturbations on a quantized background within the hybrid quantization approach. In particular, we consider a flat, homogeneous and isotropic spacetime and small tensor inhomogeneities on it. We truncate the action to second order in the perturbations. The dynamics is ruled by a homogeneous scalar constraint. We carry out a canonical transformation in the system where the Hamiltonian for the tensor perturbations takes a canonical form. The new tensor modes now admit a standard Fock quantization with a unitary dynamics. We then combine this representation with a generic quantum scheme for the homogeneous sector. We adopt a Born-Oppenheimer ansatz for the solutions to the constraint operator, previously employed to study the dynamics of scalar inhomogeneities. We analyze the approximations that allow us to recover, on the one hand, a Schrödinger equation similar to the one emerging in the dressed metric approach and, on the other hand, the ones necessary for the effective evolution equations of these primordial tensor modes within the hybrid approach to be valid. Finally, we consider loop quantum cosmology as an example where these quantization techniques can be applied and compare with other approaches.

26 pages, minor corrections and typos, bibliography updated

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• Loop Quantum Cosmology: A brief review
• Backreaction in Cosmology
• Hamiltonian diagonalization in hybrid quantum cosmology
• Non-adiabatic Evolution of Primordial Perturbations and non-Gaussinity in Hybrid Approach of Loop Quantum Cosmology
• Phenomenological implications of modified loop cosmologies: an overview
• The Born-Oppenheimer approach to Quantum Cosmology
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• Predictions for the CMB from an anisotropic quantum bounce
• Analytical investigation of pre-inflationary effects in the primordial power spectrum: From General Relativity to hybrid Loop Quantum Cosmology
• Observational consequences of Bianchi I spacetimes in loop quantum cosmology
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• Loop quantum cosmology: relation between theory and observations
• Fermions in Hybrid Loop Quantum Cosmology
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• Primordial perturbations in the Dapor-Liegener model of hybrid loop quantum cosmology
• Backreaction of fermionic perturbations in the Hamiltonian of hybrid loop quantum cosmology
• Perturbations in Quantum Cosmology: The Continuum Limit in Fourier Space
• Mass of cosmological perturbations in the hybrid and dressed metric formalisms of Loop Quantum Cosmology for the Starobinsky and exponential potentials
• Asymptotic diagonalization of the fermionic Hamiltonian in hybrid loop quantum cosmology
• The time-dependent mass of cosmological perturbations in loop quantum cosmology: Dapor-Liegener regularization
• Estimation of imprints of the bounce in loop quantum cosmology on the bispectra of cosmic microwave background
• Unique fermionic vacuum in de Sitter spacetime from hybrid quantum cosmology
• Alternative effective mass functions in the modified Mukhanov-Sasaki equation of loop quantum cosmology
• Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology
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