Quantum Gravitational Contributions to the Cosmic Microwave Background Anisotropy Spectrum

Kiefer, Claus; Krämer, Manuel

doi:10.1103/physrevlett.108.021301

Cited by 125 publications

(182 citation statements)

References 25 publications

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“…For example, applications of the covariant theory lead to detailed predictions for the cross sections of various scattering processes [8], but such phenomena (if any) occur at energy scales inaccessible to observations, and also the effects of Planck-scale physics on cosmology, e.g., the cosmic microwave background radiation and its anisotropy spectrum [9][10][11][12][13], are not yet easily accessible to observations, although cosmology offers possibly the best chances for testing quantum gravity [14].…”

Section: Introductionmentioning

confidence: 99%

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

et al. 2015

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Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist.

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Section: Introductionmentioning

confidence: 99%

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

et al. 2015

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“…We observe that if one identifies Ψ = e ī h S , with S given by (17), and substitutes in Eq. (1) the results (18) and (19) …”

Section: Geometrodynamical Approachmentioning

confidence: 99%

“…The first geometrodynamical approach by Brizuela, Kiefer and Kramer (henceforth BKK) [16,17] is examined in detail in Section 2, in particular with the aim of comparing it with our, above mentioned, traditional BO method which, in contrast, does not suffer from unitarity violating difficulties.…”

Section: Introductionmentioning

confidence: 99%

The Born–Oppenheimer method, quantum gravity and matter

Kamenshchik

Tronconi

Venturi

2017

Class. Quantum Grav.

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Abstract. We illustrate and examine diverse approaches to the quantum matter-gravity system which refer to the Born-Oppenheimer (BO) method. In particular we first examine a quantum geometrodynamical approach introduced by other authors in a manner analogous to that previously employed by us, so as to include back reaction and non-adiabatic contributions. On including such effects it is seen that the unitarity violating effects previously found disappear. A quantum loop space formulation (based on a hybrid quantisation, polymer for gravitation and canonical for matter) also refers to the BO method. It does not involve the classical limit for gravitation and has a highly peaked initial scalar field state. We point out that it does not resemble in any way to our traditional BO approach. Instead it does resemble an alternative, canonically quantised, non BO approach which we have also previously discussed.

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“…Following the approach presented in [10,11], and also used in [12,13], the next step of the analysis involves a power expansion in the inverse of the squared Planck mass m 2 P . At leading order, one recovers the Hamilton-Jacobi equation, which encodes the classical dynamics of the system.…”

Section: Quantization and Semiclassical Approximationmentioning

confidence: 99%

Quantum-Gravitational Effects on Primordial Power Spectra in Slow-Roll Inflationary Models

Brizuela¹,

Krämer

2018

Galaxies

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Abstract:We review the computation of the power spectra of inflationary gauge-invariant perturbations in the context of canonical quantum gravity for generic slow-roll models. A semiclassical approximation, based on an expansion in inverse powers of the Planck mass, is applied to the complete Wheeler-DeWitt equation describing a perturbed inflationary universe. This expansion leads to a hierarchy of equations at consecutive orders of the approximation and allows us to write down a corrected Schrödinger equation that encodes information about quantum-gravitational effects. The analytical dependence of the correction to the power spectrum on the wavenumber is obtained. Nonetheless, some numerical work is needed in order to obtain its precise value. Finally, it is shown that the correction turns out to be positive, which leads to an enhancement of the power spectrum especially prominent for large scales. We will also discuss whether this correction leads to a measurable effect in the cosmic microwave background anisotropies.

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Quantum Gravitational Contributions to the Cosmic Microwave Background Anisotropy Spectrum

Cited by 125 publications

References 25 publications

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

The Born–Oppenheimer method, quantum gravity and matter

Quantum-Gravitational Effects on Primordial Power Spectra in Slow-Roll Inflationary Models

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