Non-gaussianities and the Stimulated creation of quanta in the inflationary universe

TL;DR

The paper investigates how a non-vacuum initial state for inflaton perturbations, modeled as a density operator $\rho$, alters inflationary predictions via stimulated quantum creation. It derives modified scalar power spectra and bispectra, showing that initial quanta enhance the spectrum by a factor $1+\mathrm{Tr}[\rho N_k]+\mathrm{Tr}[\rho N_{-k}]$ and can dramatically boost squeezed-limit non-Gaussianities with $f_{NL}^{\rho}/f_{NL}^{0}$ scaling as $k_1/k_3$. These effects persist through inflation and into the observable epoch, suggesting that measurements of non-Gaussianity—particularly in the squeezed configuration—can constrain pre-inflationary physics and the initial quantum state. The work highlights that, in contrast to the standard vacuum assumption, single-field inflation with a non-vacuum initial state can produce sizable non-Gaussian signals, offering a pathway to infer the early-state physics from CMB and LSS data. All results are derived within a single-field slow-roll framework, with backreaction and renormalization constraints ensuring the initial occupation numbers remain physically viable.

Abstract

Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator $ρ$ describing an initial mixed state that includes probabilities for nonzero numbers of scalar perturbations to be present at early times during inflation. We analyze the primordial bispectrum for general configurations of the three different momentum vectors in its arguments. We find that the initial presence of quanta can significantly enhance non-gaussianities in the so-called squeezed limit. Our results show that an observation of non-gaussianities in the squeezed limit can occur for single-field inflation when the state in the very early inflationary universe is not the vacuum, but instead contains early-time perturbations. Valuable information about the initial state can then be obtained from observations of those non-gaussianities.