Abstract
It was pointed out recently that in some inflationary models quantum loops containing a scalar of mass $m$ that couples to the inflaton can be the dominant source of primordial non-Gaussianities. We explore this phenomenon in the simplest such model focusing on the behavior of the primordial curvature fluctuations for small $m/H$. Explicit calculations are done for the three and four point curvature fluctuation correlations. Constraints on the parameters of the model from the CMB limits on primordial non-Gaussianity are discussed. The bi-spectrum in the squeezed limit and the tri-spectrum in the compressed limit are examined. The form of the $n$-point correlations as any partial sum of wave vectors get small is determined.
Highlights
An inflationary era in the early Universe is a popular possibility for the solution of the horizon and flatness problems [1]
This exponential expansion inflates the size of regions that were in causal contact to enormous size, solving the horizon problem. It exponentially increases the physical wavelength of perturbations with fixed comoving wavelength, causing the density perturbations that arise from quantum fluctuations and are relevant for large-scale structure and the cosmic microwave background radiation (CMB) to have wavelengths that are well outside the horizon when inflation ends
We have examined the primordial curvature perturbations in an inflationary cosmology where the inflaton φ couples to an additional scalar field s with mass m ≪ H through the nonrenormalizable interaction gμν∂μφ∂νφs2=4Λ2
Summary
An inflationary era in the early Universe is a popular possibility for the solution of the horizon and flatness problems [1]. As such the power spectrum for fluctuations in their number density can be enhanced, at low wave vectors, if there are non-Gaussian primordial curvature correlations (generated in the inflationary era) that are enhanced as a single wave vector or partial sum of wave vectors go to zero [3,4,5,6]. For the three- and four-point primordial curvature correlations the dominant enhancements occur in the squeezed and compressed limits, respectively These enhancements in the galaxy number density power spectrum (and bispectrum [7]) at very small wave vectors are sometimes called scale-dependent biases and have been studied extensively in quasi-single field inflation (QSFI [8]), which contains an additional scalar degree of freedom s with mass m.
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