Choice of vacuum state and the relation between inflationary and Planck scales

Abstract

Recent observations about the cosmic microwave background evidence a clear discrepancy between the scale of inflation and the Planck scale expected in the conventional inflationary picture, based on simple chaotic inflationary models. This paper explores a possible resolution of this conflict by considering a slight modification of the standard general relativity scenario, which naturally incorporates a cutoff scale consistent with the observations. This last scale of power suppression appears by the combined effect of the preinflationary background dynamics and an associated initial vacuum state for the cosmological perturbations which differs from the conventional Bunch-Davies state of slow-roll inflation. We revise and correct previous discussions in the literature about the relation between this scale and the scale corresponding to the onset of inflation. The mechanism that produces this cutoff is intimately related to the criterion determining a privileged vacuum state for the primordial perturbations. We adhere to a recent proposal based on an asymptotic diagonalization of the Hamiltonian of the perturbations and leading to a non-oscillatory primordial power spectrum. With this choice, we are able to investigate analytically the model, studying in detail some physically interesting cases. These analytic calculations provide further support to our arguments about the relation between the different scales of the system.