Model independent prediction of the spectral index of primordial quantum fluctuations

Abstract

One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for cosmological scalar perturbations. This tilt is understood as a consequence of a quasi de Sitter classical equation of state describing the inflationary dark energy dominated era. Here, following previous work, we find a departure of scale invariance for the quantum Fisher information associated to de Sitter vacuum for scalar quantum spectator modes. This gives rise to a purely quantum cosmological tilt with a well defined dependence on energy scale. This quantum tilt is imprinted, in a scale dependent energy uncertainty for the spectator modes. The effective quasi de Sitter description of this model independent energy uncertainty uniquely sets the effective quasi de Sitter parameters (i.e., the small deviation from the cosmological constant equation of state) at all energy scales. In particular, in the slow-roll regime characterized by an almost constant ϵ, the quantum Fisher — model independent — prediction for the spectral index is n s = 0.9672. Moreover, the energy scale dependence of the quantum cosmological tilt implies the existence of a cosmological phase transition at energies higher than the CMB scale and of the order of 1 Mpc-1 where the tilt goes from red into blue. This strongly suggest the existence of a pre-inflationary phase where the effective scalaron contributes to the spectral index as normal relativistic matter and where the corresponding growth of the power spectrum can result in dark matter in the form of small mass primordial black holes. The source and features of the quantum cosmological tilt leading to these predictions are determined by the entanglement features of the de Sitter α- vacuum states.