Ultra Slow-Roll Inflation and the non-Gaussianity Consistency Relation (1211.0083v1)

Abstract: Ultra slow-roll inflation has recently been used to challenge the non-Gaussianity consistency relation. We show that this inflationary scenario belongs to a one parameter class of models and we study its properties and observational predictions. We demonstrate that the power spectrum remains scale-invariant and that the bi-spectrum is of the local type with fnl=5(3-ns)/4 which, indeed, represents a modification of the consistency relation. However, we also show that the system is unstable and suffers from many physical problems among which is the difficulty to correctly WMAP normalize the model. We conclude that ultra slow-roll inflation remains a very peculiar case, the physical relevance of which is probably not sufficient to call into question the validity of the consistency relation.

• The paper introduces an extension of ultra slow-roll inflation models that challenge conventional non-Gaussianity predictions in CMB observations.
• It demonstrates that the ultra slow-roll regime, while preserving scale invariance, suffers from intrinsic instability due to growing quantum fluctuations.
• The study underscores the limitations of the Maldacena consistency relation, revealing that USR inflation can yield a detectable non-Gaussian parameter of order one.

Overview of Ultra Slow-Roll Inflation and the Non-Gaussianity Consistency Relation

The paper, "Ultra Slow-Roll Inflation and the Non-Gaussianity Consistency Relation," authored by Jérôme Martin, Hayato Motohashi, and Teruaki Suyama, presents a thorough examination of the ultra slow-roll inflation scenario within the context of non-Gaussianity in the cosmic microwave background (CMB). The paper challenges the traditional consistency relation attributed to Maldacena, which links the scalar spectral index to non-Gaussian features in the simplest inflationary models.

Theoretical Framework and Findings

The research investigates a one-parameter family of inflationary models generalized from the ultra slow-roll (USR) regime, originally proposed in prior studies. Ultra slow-roll inflation is characterized by a scalar field's motion on a potential so flat that the usual slow-roll approximations are violated, with one of the horizon-flow parameters being of order one, while the other remains negligible. The authors discuss the implications of this setup on the power spectrum and investigate its stability.

A distinctive contribution of the paper is the interactive exploration of the USR regime, showing that although scale invariance can be preserved in the power spectrum, the system suffers from intrinsic instability. The curvature perturbation's quantum fluctuations grow steadily, leading to significant implications for the primordial non-Gaussianity signal.

Key Results on Non-Gaussianity

In stark contrast to slow-roll scenarios, USR inflation leads to a non-Gaussianity parameter, f_NL, of order one, which is generally higher than predicted by the Maldacena consistency relation in slow-roll inflationary models. This finding suggests that even in the presence of a single inflaton field with a standard kinetic term, the paradigm of USR can cause deviations resulting in a detectable non-Gaussian signature in the CMB.

Constraints and Implications

The paper highlights several challenges and physical difficulties inherent in realizing USR inflation:

1. Stability Issues: The USR solution is inherently unstable, tending towards traditional slow-roll behavior after only a few e-folds unless finely-tuned initial conditions are enforced.
2. Normalization Challenges: The need to match the observed amplitude of CMB fluctuations requires very low mass scales in the inflaton potential, potentially conflicting with established bounds such as those from Big Bang Nucleosynthesis.
3. Quantum Effects: Given the flatness of the potential, quantum corrections could dominate, posing difficulties in sustaining a classical trajectory through the USR phase for the typically required 60 e-folds.

Future Directions

Moving forward, this work suggests the necessity of exploring inflationary models that balance these theoretical insights with observational constraints. This could involve hybrid models where USR is part of a broader inflationary potential, or further exploration of quantum gravitational effects in such scenarios.

The paper underscores the robustness of the Maldacena non-Gaussianity consistency relation, as violating it seems achievable only under constrained and physically intricate circumstances that introduce additional layers of complexity. As such, comprehensive observational campaigns, like Planck, remain pivotal in potentially distinguishing these nuanced theoretical predictions from simpler inflationary templates.