Quantum Gravity Corrections to the Inflationary Spectrum in a Bohmian Approach

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 ${\hslash }^2$. 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 ${\hslash }^2$ 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.