Quantum Gravitational Contributions to the CMB Anisotropy Spectrum

Abstract

We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the CMB anisotropy spectrum. The non-observation so far of such corrections translates into an upper bound on the energy scale of inflation.

4 pages, v3: sign error in Eq. (5) and its consequences corrected

References in corpus (6)

• Universality of Quantum Gravity Corrections
• CMBPol Mission Concept Study: Probing Inflation with CMB Polarization
• Observational constraints on loop quantum cosmology
• Observational test of inflation in loop quantum cosmology
• Quantum geometrodynamics: whence, whither?
• Effective Field Theory of Gravity: Leading Quantum Gravitational Corrections to Newtons and Coulombs Law

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