Generation and Characterization of Large Non-Gaussianities in Single Field Inflation (0801.3295v2)

Abstract: Inflation driven by a single, minimally coupled, slowly rolling field generically yields a negligible primordial non-Gaussianity. We discuss two distinct mechanisms by which a non-trivial potential can generate large non-Gaussianities. Firstly, if the inflaton traverses a feature in the potential, or if the inflationary phase is short enough so that initial transient contributions to the background dynamics have not been erased, modes near horizon-crossing can acquire significant non-Gaussianities. Secondly, potentials with small-scale structure may induce significant non-Gaussianities while the relevant modes are deep inside the horizon. The first case includes the "step" potential we previously analyzed while the second "resonance" case is novel. We derive analytic approximations for the 3-point terms generated by both mechanisms written as products of functions of the three individual momenta, permitting the use of efficient analysis algorithms. Finally, we present a significantly improved approach to regularizing and numerically evaluating the integrals that contribute to the 3-point function.

• The paper demonstrates that features in the inflaton potential markedly amplify the bispectrum, producing substantial non-Gaussianity signatures.
• The paper reveals that non-attractor initial conditions transiently boost non-Gaussian signals, though cosmic variance limits their observational relevance.
• The paper introduces analytic approximations and efficient numerical methods that advance the design of optimal CMB estimators for detecting these effects.

Overview of Large Non-Gaussianities in Single Field Inflation

The paper "Generation and Characterization of Large Non-Gaussianities in Single Field Inflation" investigates how non-Gaussianities can arise within the context of single-field slow-roll inflation, which typically yields negligible non-Gaussianity. The authors identify two distinct mechanisms that can generate significant non-Gaussianities in single field models: the presence of a feature in the inflaton potential and the influence of transient dynamics at the onset of inflation.

Mechanisms of Non-Gaussianity Generation

1. Features in the Inflaton Potential: When the inflaton encounters a feature in its potential, such as a step or a ripple, a localized violation of the slow-roll condition occurs. This departure leads to an amplification of the 3-point correlation functions, or bispectrum, which characterizes non-Gaussianities. The authors analyze two specific cases: a step potential and a sinusoidal modulation of the potential. For the step potential, they approximate the bispectrum using analytic forms that account for the oscillatory behavior induced by the feature. The paper demonstrates that such features produce a bispectrum significantly larger than typical results in standard smooth potentials.
2. Non-Attractor Initial Conditions: Short inflationary phases prior to the onset of slow-roll can leave an imprint when modes of interest in the Cosmic Microwave Background (CMB) leave the horizon. Initial conditions that deviate from the slow-roll attractor can lead to enhanced non-Gaussianities. However, the paper argues that even dramatic enhancements fall short of being observationally significant due to cosmic variance, especially on the largest scales.
3. Resonance Inside the Horizon: A second mechanism involves potentials with oscillatory structures that create a resonance effect while the modes are deep inside the horizon. The authors discuss how these resonances introduce a new, sub-horizon scale that enhances the bispectrum's amplitude. The analysis leads to a prediction of characteristic scale-dependent oscillations in the bispectrum, which differ from those created by the features discussed in the first mechanism.

Implications and Future Directions

The analytical results obtained provide factorizable forms of the bispectrum, which are computationally advantageous and may inform the design of optimal estimators to search for these signatures in CMB data. Practically, distinguishing between these mechanisms requires careful analysis of CMB data, leveraging their distinct scale-dependences and amplitudes.

Theoretically, the findings encourage further exploration of extensions to the standard single-field paradigm. Multi-field inflationary models and models with more general kinetic terms, such as DBI or k-inflation, are potential candidates for generating substantial non-Gaussianities and require thorough investigation.

Numerical Methods and Validation

The paper meticulously describes a numerical method for integrating the equations governing the 3-point function, addressing the challenges posed by oscillatory integrands through an efficient regularization technique. This allows for an accurate and tractable evaluation of non-Gaussian signatures from complex potentials.

Overall, this work contributes significant insights into the potential for single-field inflation to produce observable non-Gaussianities and lays the groundwork for future theoretical and observational studies in this area. The analytic approximations presented capture essential features of the bispectrum and can be refined for closer numerical congruence, an undertaking that the authors plan to explore in future work.