Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation : the de Sitter case

We present detailed calculations for quantum-gravitational corrections to the power spectra of gauge-invariant scalar and tensor perturbations during inflation. This is done by performing a semiclassical Born-Oppenheimer type of approximation to the Wheeler-DeWitt equation, from which we obtain a Schrödinger equation with quantum-gravitational correction terms. As a first step, we perform our calculation for a de Sitter universe and find that the correction terms lead to an enhancement of power on the largest scales.