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 ${\hslash }^2$. 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.

19 pages, 4 figures; discussion expanded and references added; matching the published version

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