Non-Vacuum Initial States for Cosmological Perturbations of Quantum-Mechanical Origin

Abstract

In the context of inflation, non-vacuum initial states for cosmological perturbations that possess a built in scale are studied. It is demonstrated that this assumption leads to a falsifiable class of models. The question of whether they lead to conflicts with the available observations is addressed. For this purpose, the power spectrum of the Bardeen potential operator is calculated and compared with the CMBR anisotropies measurements and the redshift surveys of galaxies and clusters of galaxies. Generic predictions of the model are: a high first acoustic peak, the presence of a bump in the matter power spectrum and non-Gaussian statistics. The details are controlled by the number of quanta in the non-vacuum initial state. Comparisons with observations show that there exists a window for the free parameters such that good agreement between the data and the theoretical predictions is possible. However, in the case where the initial state is a state with a fixed number of quanta, it is shown that this number cannot be greater than a few. On the other hand, if the initial state is a quantum superposition, then a larger class of initial states could account for the observations, even though the state cannot be too different from the vacuum. Planned missions such as the MAP and Planck satellites and the Sloan Survey, will demonstrate whether the new class of models proposed here represents a viable alternative to the standard theory.