Quasi-Single Field Inflation and Non-Gaussianities (0911.3380v4)

Abstract: In quasi-single field inflation models, massive isocurvature modes, that are coupled to the inflaton and have mass of order the Hubble parameter, can have nontrivial impacts on density perturbations, especially non-Gaussianities. We study a simple example of quasi-single field inflation in terms of turning inflaton trajectory. Large bispectra with a one-parameter family of novel shapes arise, lying between the well-known local and equilateral shape. The trispectra can also be very large and its magnitude tNL can be much larger than fNL squared.

• The paper demonstrates that quasi-single field dynamics with turning trajectories and massive isocurvature modes produce significant non-Gaussian signatures.
• It reveals that the bispectrum exhibits unique intermediate shapes, bridging local and equilateral forms, while trispectra contributions may dominate over conventional measures.
• The authors employ the in-in formalism and Feynman diagrams to ensure robust convergence in calculating the transfer of perturbations, enhancing theoretical precision.

Quasi-Single Field Inflation and Non-Gaussianities: A Detailed Overview

The paper "Quasi-Single Field Inflation and Non-Gaussianities" represents a rigorous examination of models that go beyond the canonical single field inflation paradigm by incorporating massive isocurvature modes. These modes, though secondary, introduce significant non-linear corrections to the inflation dynamics, specifically influencing non-Gaussianities in the primordial perturbations.

Quasi-single field inflation is an intriguing construct where the field dynamics involve a primary inflationary direction coupled with one or more isocurvature directions. The masses of these isocurvature modes are on the order of the Hubble parameter, $H$. Despite being massive, these isocurvature modes can interact with the inflaton through a turning trajectory, leading to measurable effects on the cosmological observables. This paper articulates this concept using a specific model where the important dynamic feature is the coupling between inflaton and isocurvatons through a non-straight inflaton trajectory. This coupling produces large non-Gaussianities, characterized by novel shapes in the bispectra and trispectra of cosmic perturbations.

Key Contributions and Findings

1. Dynamic Structure: The paper elaborates on the quasi-single field inflation where an inflaton follows a turning trajectory. This dynamic is facilitated by an isocurvature mode with a mass $m \sim H$. As such, the perturbations do not decay rapidly after crossing the horizon, resulting in large non-Gaussianities.
2. Non-Gaussianities: Significant non-Gaussianity is a haLLMark of these models, resulting from the interactions across the field's mass and trajectory. The bispectrum's shape is an original contribution of this work, lying between the traditionally considered local and equilateral forms.
3. Trispectra and Higher Order Interactions: The analysis extends to trispectra, revealing potentially dominant contributions when compared to $f_{NL}^2$, where $f_{NL}$ represents a conventional measure of bispectrum amplitude.
4. Methodology: The authors employ the in-in formalism and Feynman diagrams, emphasizing transfer vertices from isocurvature to adiabatic perturbations. They deploy a mixed approach using factorized and commutator forms for robust convergence of integrals, enhancing computational feasibility.
5. Significance of the Isocurvature Mass ( $\nu$ Parameter): The resulting non-Gaussianity's shape bifurcates based on mass: heavier isocurvatons ($m/H > \sqrt{2}$) produce equilateral-like shapes, while lighter ones ($3/2 > \nu > 1/2$) resemble local forms. An interesting behavior is observed near $\nu = 0$ where the shape transforms markedly affecting observational characteristics.

Implications and Speculations

The research presented in this paper holds profound implications for cosmology, especially in preparation for high-precision data analyses from upcoming experiments. Non-Gaussianity is not only a potential smoking gun for inflationary theory verification, but it also provides fine detail into multi-field dynamics.

From a theoretical standpoint, the paper bridges the gap between simpler single-field and complex multi-field paradigms, pushing the boundaries on the types and strengths of interactions permissible in early universe inflationary models. This could also influence string theory models and constructions facing challenges posed by UV completion.

Practically, the continual development of data analysis techniques sensitive to these intermediate shapes could enable better observational constraints or detections of these non-Gaussian signals in new survey data. Furthermore, the perturbative methods and formalism adjustments guide methodological advancements for handling emerging complexities in cosmological perturbation theory.

Conclusion

Quasi-single field inflation presents a competitive framework in understanding inflation's subtleties, offering vital insights into non-Gaussianity signatures and their scale dependence. As theoretical and observational tools mature, such models serve as crucial exploratory paths to map the rich landscape of early universe phenomena, potentially unlocking new physics beyond the standard models of cosmology.