Violation of non-Gaussianity consistency relation in a single field inflationary model (1210.3692v2)

Abstract: In this paper we present a simple, toy model of single field inflation in which the standard non-Gaussianity consistency condition is violated. In this model the curvature perturbations on super-horizon scales are not conserved and the decaying modes of perturbations are not negligible in the non-atractor phase. As a result a large local non-Gaussianity can be obtained in the squeezed limit which violates the standard non-Gaussianity consistency condition for the single field models.

• The paper demonstrates that a single-field inflationary model can breach the standard non-Gaussianity consistency relation by producing a surprisingly high fNL value.
• The study underscores that non-conservation of curvature perturbations during a non-attractor phase allows decaying modes to generate significant local non-Gaussianity.
• The findings imply that observable large non-Gaussianity could signal unconventional inflationary dynamics, urging a reexamination of standard single-field models.

Analysis of the Violation of Non-Gaussianity Consistency in a Single-Field Inflationary Model

The paper by Namjoo, Firouzjahi, and Sasaki presents a theoretical investigation into the emergence of large local non-Gaussianity within a single-field inflationary model, highlighting violations of the conventional non-Gaussianity consistency relation. Here, the authors introduce a model where the standard inflationary conditions do not apply, resulting in an intriguing challenge to widely accepted theoretical predictions concerning single-field models.

The paper focuses on a toy model of single-field inflation, characterized by a constant potential $V_0$. The significance of this model lies in its deviation from the attractor phase typically assumed in inflationary paradigms. Notably, during this non-attractor phase, curvature perturbations do not remain conserved on super-horizon scales, contrary to standard expectations. This lack of conservation permits the decaying modes of perturbations to exert a substantial influence, enabling them to generate significant local non-Gaussianity in the squeezed limit, a regime where conventional consistency relations predict negligible non-Gaussianity for single-field scenarios.

Key Findings

1. Consistency Relation Violation: The model demonstrates a notable violation of the standard non-Gaussianity consistency condition. Conventionally, this relation predicts that in the squeezed limit, the amplitude of non-Gaussianity ($f_{NL}$) is related to slow-roll parameters $\eta$ by $\frac{3}{5}f_{NL} = \frac{\eta}{4}$. However, the paper shows that $f_{NL}$ obtains a value of $+\frac{5}{2}$, clearly violating the conventional prediction.
2. Perturbation Dynamics: This violation is attributed primarily to the dynamics during the non-attractor phase where the decaying modes dominate. Specifically, the curvature perturbation evolves in such a way that its non-conservation on super-horizon scales facilitates enhanced non-Gaussianity, diverging from typical single-field models where perturbations are conserved.
3. Observational Implications: The proposed model suggests that large local non-Gaussianities might be detectable in observational data, providing an alternative pathway to identifying the inflationary dynamics beyond standard attractor solutions.

Theoretical and Practical Implications

The theoretical implications of this paper are significant, as they challenge the broadly held assumption that single-field inflationary models necessarily adhere to the non-Gaussianity consistency relation. This paper provides a compelling example where deviations from the attractor behavior can lead to departures from these expected outcomes. Practically, this suggests that inflationary models should not be prematurely classified as multi-field or exotic based solely on observational evidence of large non-Gaussianities.

Future Directions in AI and Cosmology

In future research, it would be essential to explore more realistic models that incorporate mechanisms for ending inflation smoothly, known as the graceful exit problem. A plausible incorporation would potentially involve transitioning to a conventional slow-roll phase with a modified potential to feasibly end inflation. Moreover, as AI and machine learning increasingly contribute to data analysis in cosmology, these tools could be pivotal in distinguishing signatures of non-attractor behaviors in cosmic microwave background observations.

In conclusion, this paper enriches the theoretical landscape by suggesting a previously unexplored facet of single-field inflationary models that escape standard classification. The paper underscores the vitality of theoretical innovation and meticulous scrutiny necessary to advance our understanding of the early universe's fundamental processes.