Quantum Gravity Corrections to the inflationary spectrum in a Bohmian approach

TL;DR

This paper applies a Bohmian interpretation to quantum cosmology, incorporating quantum corrections into the inflationary spectrum, and analyzes how these modifications affect the scale-invariance and spectral index of primordial fluctuations.

Contribution

It introduces a Bohmian approach to quantum cosmology with quantum corrections, providing a new way to compute inflationary spectra with $bar^2$ effects included.

Findings

Quantum corrections modify the inflationary spectrum.

The spectrum deviates from scale invariance due to quantum effects.

The spectral index and its running are affected by $bar^2$ corrections.

Abstract

A precise interpretation of the Universe wave function is forbidden in the spirit of the Copenhagen School since a precise notion of measure operation cannot be satisfactorily defined. Here we propose a Bohmian interpretation of the isotropic Universe quantum dynamics, in which the Hamilton-Jacobi equation is restated by including quantum corrections, which lead to a classical trajectory containing effects of order $\hbar^2$. This solution is then used to determine the spectrum of gauge-invariant quantum fluctuations living on the obtained background model. The analysis is performed adopting the wave function approach to describe the fluctuation dynamics, which gives a time-dependent harmonic oscillator for each Fourier mode and whose frequency is affected by the $\hbar^2$ corrections. The properties of the emerging spectrum are discussed, outlining the modification induced with respect to the scale-invariant result and the hierarchy of the spectral index running is discussed.