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.
Highlights
The lack of experimental guidance is still one of the main obstacles to advance in the construction and verification of the ultimate theory of quantum gravity [1]
During the inflationary phase of the primordial universe energies close to the Planck scale were present and the conditions for structure formation were set, which makes it plausible that Planck-scale physics might be directly related to the anisotropies of the cosmic microwave background (CMB) and, be observable by our telescopes [2]
In this conference proceedings contribution based on our previous work published in [3,4], we review a computation of the quantum-gravity effects in the power spectra of both gauge-invariant scalar and tensor perturbations
Summary
The lack of experimental guidance is still one of the main obstacles to advance in the construction and verification of the ultimate theory of quantum gravity [1]. During the inflationary phase of the primordial universe energies close to the Planck scale were present and the conditions for structure formation were set, which makes it plausible that Planck-scale physics might be directly related to the anisotropies of the cosmic microwave background (CMB) and, be observable by our telescopes [2]. In this conference proceedings contribution based on our previous work published in [3,4], we review a computation of the quantum-gravity effects in the power spectra of both gauge-invariant scalar and tensor perturbations. In order to keep the potential of the inflaton field as generic as possible, all the computations will be performed assuming a slow-roll regime
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