Quantum Cosmology and the Inflationary Spectra from a Non-Minimally Coupled Inflaton

Abstract

We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation governing the quantum evolution of the inflationary perturbations is derived on a de Sitter background. Moreover the problem of the introduction of time is addressed and a generalized method, with respect to that used for the minimal coupling case, is illustrated. Such a generalized method can be applied to the universe wave function when, through the Born-Oppenheimer factorization, we decompose it into a part which contains the minisuperspace degrees of freedom and another which describes the perturbations.

arXiv comment24 pages, no figures

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Cited by in corpus (10)

• De Sitter solutions in Einstein-Gauss-Bonnet gravity
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• WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings
• Study of the Inflationary Spectrum in the Presence of Quantum Gravity Corrections
• Quantum gravity corrections to the matter dynamics in the presence of a reference fluid
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• Time and Evolution in Quantum and Classical Cosmology
• Born-Oppenheimer meets Wigner-Weyl in Quantum Gravity
• Quantum Gravity Corrections to the inflationary spectrum in a Bohmian approach
• Fermionic quantum cosmology as a framework for resolving type IV singularities