# A moment approach to compute quantum-gravity effects in the primordial universe

## TL;DR

This paper introduces a moment-based method to calculate quantum-gravity corrections to inflationary power spectra, revealing an enhancement at large scales and aligning with previous semiclassical approaches.

## Contribution

It develops a novel moment approach to analyze quantum-gravity effects in the early universe, providing analytical and numerical results consistent with prior studies.

## Key findings

- Quantum-gravity corrections enhance large-scale power spectra.
- The moment approach aligns with previous semiclassical results.
- Numerical analysis confirms the analytical approximation.

## Abstract

An approach to compute quantum-gravity corrections to the scalar and tensorial power spectra of the inflationary perturbations is presented. The analysis of the Wheeler-DeWitt equation is performed by a decomposition of the wave function into its infinite set of moments, which must obey certain system of (first-class) constraints. Considering a semiclassical approximation, the system is truncated at second order in moments and an appropriate gauge-fixing condition is introduced, which allows us to interpret the scale factor of the universe as an internal time. The evolution of the different fluctuations and correlations is then explicitly considered for a de Sitter universe. An approximate analytical solution is obtained for the corrections of the power spectra, which produces an enhancement of power for large scales. Remarkably, the result is in agreement with previous studies in the literature that made use of very different semiclassical approximations. Finally, the numerical implementation of the system is also considered to verify the validity of the analytical solution.