Pre-slow-roll initial conditions: Large scale power suppression and infrared aspects during inflation

Abstract

If the large scale anomalies in the temperature power spectrum of the cosmic microwave background are of primordial origin, they may herald modifications to the slow roll inflationary paradigm on the largest scales. We study the possibility that the origin of the large scale power suppression is a modification of initial conditions during slow roll as a result of a pre-slow roll phase during which the inflaton evolves rapidly. This stage is manifest in a potential in the equations for the Gaussian fluctuations during slow roll and modify the power spectra of scalar perturbations via an initial condition transfer function T (k). We provide a general analytical study of its large and small scale properties and analyze the impact of these initial conditions on the infrared aspects of typical test scalar fields. The infrared behavior of massless minimally coupled test scalar field theories leads to the dynamical generation of mass and anomalous dimensions, both depend non-analytically on T (0). During inflation all quanta decay into many quanta even of the same field because of the lack of kinematic thresholds. The decay leads to a quantum entangled state of sub and superhorizon quanta with correlations across the horizon. We find the modifications of the decay width and the entanglement entropy from the initial conditions. In all cases, initial conditions from a "fast-roll" stage that lead to a suppression in the scalar power spectrum at large scales also result in a suppression of the dynamically generated masses, anomalous dimensions and decay widths.

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

“…When the mode functions of the χ field become "super-horizon" the quantum master equation effectively describes quantum entanglement between these super-horizon modes and the sub-horizon degrees of freedom that have been traced over, in agreement with the results of ref. [18].…”

“…• Minimally coupled scalars secular and infrared enhancements: If the inflaton ("system") scalar field couples to other (environmental) scalar fields that are minimally coupled to gravity and with masses M ≪ H these "environmental" fields feature quantum fluctuations that are infrared and secularly enhanced when their wavelengths become super-Hubble [6,8,9,11,13,15,18,22].…”

“…The χ field is considered to be minimally coupled, ξ χ = 0 and nearly massless with M χ /H ≪ 1, from which it follows that as −qη → 0 (2.17) This behavior in the super-Hubble limit will lead to strong secular contributions in the long time limit. The time evolution of a density matrix initially prepared at time η 0 is given by 18) where Tr[ρ(η 0 )] = 1 and U(η, η 0 ) is the unitary time evolution of the full theory, it obeys (2.19) where H(η) is the total Hamiltonian. Writing the total Hamiltonian in terms of the free and interaction Hamiltonians as H(η) = H 0 (η) + H i (η) it is convenient to pass to the interaction picture introducing the unitary time evolution operator of the free theory U 0 (η, η 0 ) obeying (2.20) and define the density matrix in the interaction picture…”

“…Such interaction between the inflaton and other (fermionic, scalar) degrees of freedom cannot just switch-on at the end of inflation, and on physical grounds should be expected to be present even during the inflationary stage. Interactions of quantum fields in de Sitter (or nearly de Sitter) space-time have been the focus of several studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] which show strong infrared and secular effects and the possibility that the vacuum state in de Sitter space time may be unstable towards decay [26]. Non-Gaussianity is a manifestation of self-interactions of curvature perturbations and could leave an observable imprint on the cosmic microwave background, although it is argued to be small in single field slow roll inflationary models [27][28][29].…”

Looking for non-Gaussianity in all the right places: A new basis for nonseparable bispectra

“…It is usually taken to be the Bunch-Davies state, but from the point of view of treating inflation as an effective theory it is not unreasonable to consider the choice of state to be open, subject to the conditions that it allow for inflation to occur and that it be consistent with field theoretic precepts. Explicit examples of scenarios that give rise to non-Bunch-Davies initial conditions for inflation can be found in [1][2][3][4][5][6]. Assuming that the initial state is more general than the free vacuum, such as a Bogoliubov transform of the BunchDavies state or even a mixed state, we can calculate its imprint on cosmological observables like the power spectrum and bispectrum of inflationary perturbations, and in turn those of CMB temperature anisotropies [2,3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”