The Minimal Volkov - Akulov - Starobinsky Supergravity (1403.3269v2)

Abstract: We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield $X$, which is subject however to the constraint $X^2=0$ so that it describes only a Volkov - Akulov goldstino and an auxiliary field. We also construct the dual higher - derivative model, which rests on a chiral scalar curvature superfield ${\cal R}$ subject to the constraint ${\cal R}^2=0$, where the goldstino dual arises from the gauge - invariant gravitino field strength as $\gamma^{mn} {\cal D}_m \psi_n$. The final bosonic action is an $R+R^2$ theory involving an axial vector $A_m$ that only propagates a physical pseudoscalar mode.

• The paper constructs a supergravity model that meshes the Volkov–Akulov goldstino with Starobinsky inflation using a minimal chiral superfield system.
• It employs higher-derivative formulations and dual representations to capture scalaron and axion dynamics, matching key inflationary predictions.
• The work paves the way for improved computational cosmology through nilpotency constraints, offering actionable insights for future research.

An Analysis of the Volkov–Akulov–Starobinsky Supergravity Model

The paper presents a comprehensive construction of a supergravity model that incorporates the Volkov–Akulov mechanism into the Starobinsky model of inflation. This endeavor is notable for its synthesis of a minimal chiral superfield system with supergravity frameworks to create a model characterized by both the scalaron and axion fields as its scalar degrees of freedom. This adaptation presents an expressive formulation that strives to integrate supergravity theories with cosmological inflationary models, thus enveloping quantum field theories within the supergravity constructs.

Model Construction and Theoretical Innovations

The authors align their theoretical framework with the Starobinsky model, governed by its distinct R+R action, and develop a higher-derivative supergravity formalism that incorporates two key chiral superfields, denoted as the scalar curvature superfield $R$ and the chiral multiplet $X$. Within this framework, $X$ is constrained such that it exclusively describes a Volkov–Akulov goldstino, devoid of any scalars. By imposing this constraint, the otherwise complex dynamics of the chiral superfields are boiled down to a goldstino and an auxiliary field agreement.

Through the dual formulation rooted in chiral curvature superfields, the model effectively transitions from scalar to superspace density formulations. This flexibility allows the elaboration of gravitational theories that operate across traditional $R+R$ theories and advanced supergravity actions. Importantly, the use of chiral compensator fields and the intricate interplay of related identities facilitate this dual representation, enabling the reproduction of Starobinsky models within a supergravity context.

Implications and Theoretical Outcomes

Notably, the formulation shows that in the Volkov–Akulov–Starobinsky framework, the inflationary scalar potential stages an intriguing blend by combining the Starobinsky potential with the Volkov–Akulov-type goldstino. Besides its intrinsic academic interest, this formulation may also act as a prototype for further investigating cosmological phenomena through a fundamental physics perspective.

The presented work recognizes the pursuance of compatibility between supergravity models and current PLANCK data—achieving a noteworthy alignment with inflationary predictions of approximately 60 e-folds. However, due to complexities in stability and universal Kähler potential formulation, non-minimal models become necessary for ensuring dynamic equilibria during the inflationary stages. This particular aspect underscores the interplay between theoretical feasibility and phenomenological requirements.

Speculations on Future Directions

Going forward, this research points towards potential applications in understanding the origins and mechanisms behind significant cosmological processes, broadening the foundational footprint of supergravity theories. As supergravity continually interfaces with observational rigor, particularly in cosmological forecasts, these results present opportunities for leveraging higher-derivative theories and constrained multiplet techniques.

Moreover, the simplicity achieved via the eliminations inherent in the nilpotency condition of the $X$ superfield could be explored to enhance computational efficiency when simulating other cosmological models. This capability could make complex models more accessible to researchers working with numerical simulations, thus further expanding the instances where theoretical predictions and observational data coexist harmonically.

In summation, this paper offers a probable glimmer into a seamless synthesis of universal inflationary modeling with supergravity, revealing a rich topography of theoretical insights and further exploration paths.