Fermionic influence on inflationary fluctuations

Abstract

Motivated by apparent persistent large scale anomalies in the CMB we study the influence of fermionic degrees of freedom on the dynamics of inflaton fluctuations as a possible source of violations of (nearly) scale invariance on cosmological scales. We obtain the non-equilibrium effective action of an inflaton-like scalar field with Yukawa interactions (Y D,M ) to light fermionic degrees of freedom both for Dirac and Majorana fields in de Sitter space-time. The effective action leads to Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and a stochastic gaussian noise. We solve the Langevin equation in the super-Hubble limit implementing a dynamical renormalization group resummation. For a nearly massless inflaton its power spectrum of super Hubble fluctuations is enhanced, P(k; η) = (Majorana fermions, and η 0 is the renormalization scale at which the inflaton mass vanishes. The full power spectrum is shown to be renormalization group invariant. These corrections to the super-Hubble power spectrum entail a violation of scale invariance as a consequence of the coupling to the fermionic fields. The effective action is argued to be exact in a limit of large number of fermionic fields. A cancellation between the enhancement from fermionic degrees of freedom and suppression from light scalar degrees of freedom conformally coupled to gravity suggests the possibility of a finely tuned supersymmetry among these fields.

Effective field theory during inflation. II. Stochastic dynamics and power spectrum suppression

“…A Yukawa coupling between the inflaton fluctuations and fermionic fields yields an influence action in terms of self-energy and noise kernels much in the same manner as for the case studied in the previous sections. Results of this study will be reported elsewhere [63].…”

Effective field theory during inflation: Reduced density matrix and its quantum master equation

“…In this reference the equivalence between integrating out the heavy (or short wavelength) degrees of freedom in the path integral representation and the quantum master equation is established up to second order in the coupling. This equivalence and the relation to a stochastic description translate directly to the case of an FRW cosmology, these more formal aspects are relegated to a companion article [44]. In this article we obtain the quantum master equation directly and apply it to understand several physical consequences.…”

“…[43] it is shown that this approximation results from obtaining the non-equilibrium effective action in the path integral SchwingerKeldysh formulation in a consistent cumulant expansion of the trace over the environmental degrees of freedom when the initial density matrix is factorized. These aspects translate directly to an FRW cosmology in conformal time as discussed in a companion article [44]. In this article we assume (as is common in the literature) that the initial density matrix at the beginning of inflation is of the factorized form, it is clearly interesting to consider the case of initial correlations, which is postponed to further study.…”

Renormalization in open quantum field theory. Part I. Scalar field theory

“…1 Second, open relativistic QFTs are very relevant by themselves in heavy ion physics [19][20][21][22] and cosmology [23][24][25][26][27][28][29][30]. Third motivation is to better understand the apparently non-unitary evolution engendered by black holes and to give a quantitative characterization of the information loss.…”