Counting Primordial Perturbations Under a Corpuscular Cosmological Framework

A comparative analysis of two inflationary models, semi-classical inflation and corpuscular inflation, is crucial in furthering the field of inflationary cosmology. The semi-classical model of inflation is a topic of scientific debate due to its failure to account for the quantum nature of the background or the back-reaction of perturbations on it. Corpuscular cosmology, first put forth by Dvali and Gomez, describes maximally symmetric cosmological spaces as a Bose-Einstein condensate near a point of quantum criticality. The application of this purely quantum picture to the inflationary universe allows one to recover details about this epoch that the semi-classical model leaves unaddressed. According to this model, the primordial perturbations evidenced by CMB fluctuations result from the depletion of the condensate background. The objective of this project is to derive the occupation number of depleted quanta. The significance of this value lies in its comparative potential to cosmological observables such as the CMB. The derivation of the number of primordial perturbations resulting from each inflationary de Sitter patch is reported in this paper.