Quantum Gravity Corrections to the Inflationary Spectrum in a Bohmian Approach

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 ℏ2. 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 ℏ2 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.