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

Enhancements of primordial curvature fluctuations in single field inflation often involve departures from attractor trajectories in the phase space. We study enhancement/suppression of primordial fluctuations in one of the simplest models with exact background solutions for arbitrary initial conditions: a single field inflationary model with a piecewise exponential potential. We then present close to exact analytical solutions for primordial fluctuations in a general transition between two slow-roll attractors, valid whether the first slow parameter increases or decreases. The main features in the primordial spectrum are determined by the ratio of exponents of the potential. We also discuss the imprint of such features in the induced GW spectrum. Lastly, we apply the δN formalism to discuss non-Gaussianities and the tail of the probability distribution. We find that while non-Gaussianities are at most 𝒪(1) in the case of enhancement, they can be very large in the case of suppression. Our work can be easily generalized to multiple piecewise exponential potentials.

“…For an interesting discussion on the effects of one-loop corrections on large scales see refs [72,179,[181][182][183][184][185][186][187][188]…”

mentioning

confidence: 99%

An exact model for enhancing/suppressing primordial fluctuations

Domènech,

Vargas,

Vargas

2024

“…To know more about the impacts of the loop effects on the power spectrum in the light of PBH formation, see other refs. [119,120,124,[140][141][142][143][144][145]. Now, since the findings of the tree level non-Gaussianity have to be consistent with the findings of the quantum loop corrected amplitude of the primordial power spectrum, one can immediately discard both possibilities in the present scenario.…”

Section: Jcap01(2024)012 1 Introductionmentioning

confidence: 72%

Primordial non-Gaussianity from ultra slow-roll Galileon inflation

Choudhury,

Karde,

Panda

et al. 2024

We present a detailed study of the generation of large primordial non-Gaussianities during the slow-roll (SR) to ultra-slow roll (USR) transitions in the framework of Galileon inflation. We found out that due to having sharp transitions in the USR phase, which persist with a duration of Δ𝒩USR ∼ 2 e-folds, we are able to generate the non-Gaussianity amplitude of the order: |f NL| ∼ 𝒪(10-2) in the SRI, -5 < f NL < 5 in the USR, and -2 < f NL < 2 in the SRII phases. As a result, we are able to achieve a cumulative average value of |f NL| ∼ 𝒪(1). This implies that our results strictly satisfy Maldacena's no-go theorem in the squeezed limit only for SRI, while they strictly violate the same condition in both the USR and SRII phases. The non-renormalization theorem in the Galileon theory helps to support our results regarding the generation of large mass primordial black holes along with large non-Gaussianities, which we show to be dependent on the specific positions of the transition wave numbers fixed at low scales.

“…Our estimates have indicated significant one-loop corrections around the peak of the density power spectrum generated during the USR inflation. Subsequently, the work was extended to the Hartree resummation to account for the loop effects in a self-consistent manner that certainly is beyond the oneloop approximation [16], in which the momentum cutoff is set by the Hubble parameter to account for the sensitive infrared modes of superhorizon scales only in such a nearly de Sitter background [17,18]. Apart from involving V ′ (ϕ) and V ′′ (ϕ), we have also included V ′′′ (ϕ) and V [4] (ϕ) to consider the loop effects to the background equation of motion for the inflaton mean-field and the mode equation of the field perturbation.…”

Section: Jcap03(2024)008mentioning

confidence: 99%

“…Ultra-slow-roll (USR) inflation was therefore proposed, invoking a transient USR phase in the single-field inflation [11][12][13][14]. In our early works [15,16], we have considered the quantum loop effects to the primordial perturbations generated by a single scalar field during the dynamics of the SR-USR-SR inflation in the spatially flat gauge. In ref.…”

Section: Introductionmentioning

confidence: 99%

Primordial perturbations from ultra-slow-roll single-field inflation with quantum loop effects

Cheng,

Lee,

2024

Self Cite

It is known that the single-field inflation with a transient ultra-slow-roll phase can produce a large curvature perturbation at small scales for the formation of primordial black holes. In our previous work, we have considered quantum loop corrections to the curvature perturbation and found that the growth of these small-scale modes would affect the curvature perturbation at large scales probed by cosmic microwave background observation. In this work, we will further derive the constraints on the growing modes in the transition between the slow-roll and the ultra-slow-roll phases under the effect of the loop corrections. Our results would help clarify the recent controversy on whether or not the primordial-black-hole formation from the single-field inflation is ruled out at one-loop level.