Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation

TL;DR

This paper investigates quantum-gravitational corrections to inflationary perturbations during slow-roll inflation, deriving modified power spectra and tensor-to-scalar ratios, and estimating their observational significance.

Contribution

It extends previous work by analyzing quantum-gravitational effects beyond de Sitter space, incorporating slow-roll parameters into the corrections to inflationary spectra.

Findings

Quantum-gravitational corrections modify power spectra on large scales.

Corrections to the tensor-to-scalar ratio are derived at second order in slow-roll.

Estimated magnitude of corrections suggests potential observational relevance.

Abstract

We continue our study on corrections from canonical quantum gravity to the power spectra of gauge-invariant inflationary scalar and tensor perturbations. A direct canonical quantization of a perturbed inflationary universe model is implemented, which leads to a Wheeler-DeWitt equation. For this equation, a semiclassical approximation is applied in order to obtain a Schroedinger equation with quantum-gravitational correction terms, from which we calculate the corrections to the power spectra. We go beyond the de Sitter case discussed earlier and analyze our model in the first slow-roll approximation, considering terms linear in the slow-roll parameters. We find that the dominant correction term from the de Sitter case, which leads to an enhancement of power on the largest scales, gets modified by terms proportional to the slow-roll parameters. A correction to the tensor-to-scalar ratio is also found at second order in the slow-roll parameters. Making use of the available experimental data, the magnitude of these quantum-gravitational corrections is estimated. Finally, the effects for the temperature anisotropies in the cosmic microwave background are qualitatively obtained.