Quantum loop effects to the power spectrum of primordial perturbations during ultra slow-roll inflation

Abstract

We examine the quantum loop effects on the single-field inflationary models in a spatially flat Friedmann-Robertson-Walker cosmological space-time with a general self-interacting scalar field potential, which is modeled in terms of the Hubble flow parameters in the effective field theory approach. In particular, we focus on the scenarios in both slow-roll to ultra-slow-roll (SR-USR) and SR-USR-SR inflation, in which it is shown that density perturbations originated from quantum vacuum fluctuations can be enhanced at small-scales, and then potentially collapse into primordial black holes. Here our estimates indicate significant one-loop corrections around the peak of the density power spectrum in both scenarios. The induced large quantum loop effects should be confirmed by a more formal quantum field theory, and, if so, should be treated in a self-consistent manner that will be discussed.

Power spectrum of primordial perturbations during ultra-slow-roll inflation with back reaction effects

“…with M −2 P l = 8πG N set to be M −2 P l = 1, which will be restored if necessary. One shall start from the metric in the Arnowitt-Deser-Misner (ADM) form in the 3 + 1 decomposition with N the lapse function and N i the shift-vector as well as the 3 spatial dimensions metric h ij [26][27][28]. In particular, for a spatially flat Friedmann-Robertson-Walker (FRW) cosmological space-time N = 1, N i = 0, and h ij = a 2 (t)δ ij where a is a scale factor.…”

“…H is the Hubble parameter and is the Hubble flow parameter being small during the USR and SR inflations [26]. The tadpole method (see Ref.…”

“…Then the study is to extend to the USR inflation as a transition phase. In particular, when the Universe goes from the USR to SR regimes, there exists the accompanying large value of ϕ 2 due to the combined effects of the strong infrared enhancement and the spike in the power spectrum [26]. In this work, we will adopt the approach to taking into account the quantum field fluctuations ϕ 2 self-consistently by implementing the Hartree factorization.…”

“…Our presentation is organized as follows. In next section, we introduce the single-field inflationary models in a metric of the perturbed spatially flat Friedmann-Robertson-Walker (FRW) cosmological space-time starting from the Arnowitt-Deser-Misner (ADM) form by following [26]. We then separate the classical homogeneous background field (Φ 0 ) from the quantum field fluctuations (ϕ).…”

“…The background field in the FRW metric with the quantum loop corrections through ϕ 2 is derived whereas the scale factor follows the modified Friedmann equations also including the loop contributions. The equations of motion for the mode functions of ϕ can be derived from the quadratic terms of the field ϕ in the Lagrangian density as in [26] where in this work we further implement the Hartree factorization for selfconsistently taking into account ϕ 2 . The power spectrum of primordial perturbations in a spatially flat gauge can be expressed in terms of the mode functions.…”