No-Scale Supergravity Realization of the Starobinsky Model of Inflation (1305.1247v2)

Abstract: We present a model for cosmological inflation based on a no-scale supergravity sector with an SU(2,1)/U(1) Kahler potential, a single modulus T and an inflaton superfield Phi described by a Wess-Zumino model with superpotential parameters (mu, lambda). This model yields a scalar spectral index n_s and a tensor-to-scalar ratio r that are compatible with the Planck measurements for values of lambda simeq mu/3M_P. For the specific choice lambda = mu/3M_P, the model is a no-scale supergravity realization of the R+R^2 Starobinsky model.

• The paper introduces a no-scale supergravity model that embeds the Starobinsky R+R^2 inflation framework using a specific parameter choice (λ=μ/3MP).
• The model yields key cosmological predictions with a scalar spectral index of about 0.965 and a tensor-to-scalar ratio near 0.0035, aligning with Planck CMB data.
• Incorporating supersymmetry, the framework offers insights into solving the hierarchy problem and suggests potential links with string theory.

Analysis of the No-Scale Supergravity Realization of the Starobinsky Model of Inflation

In the presented paper, the authors propose a no-scale supergravity model, integrating the Starobinsky model of inflation within a theoretical construct that intersects cosmology with other particle physics frameworks. This builds upon the realization of the Starobinsky $R+R^2$ model fundamentally characterized by gravitational dynamics, leveraging the mathematical elegance of a supergravity formulation.

Core Framework

The research begins by embedding the Starobinsky model within a no-scale supergravity sector, using an SU(2,1)/SU(2) $\times$ U(1) Kähler potential. The model utilizes a single modulus field, $T$, alongside an inflaton superfield $\Phi$, describable through a Wess-Zumino model characterized by the superpotential parameters $\mu$ and $\lambda$. A critical point is that for the choice $\lambda = \mu/3M_P$, where $M_P$ represents the Planck mass, the model operates as a no-scale supergravity realization of the $R+R^2$ Starobinsky model.

Compatibility with Planck Data

In their analysis, the authors emphasize the model’s alignment with the Planck cosmic microwave background (CMB) data, specifically the metrics concerning the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$. The paper articulates that for specific parameter choices, like $\lambda \simeq \mu/3M_P$, the predictions for $n_s \approx 0.965$ and $r \approx 0.0035$ fall within the empirically supported range. The adherence to empirical parameters without needing fine-tuning highlights the model’s potential validity.

Implications and Theoretical Underpinnings

The inclusion of supersymmetry inherently suggests promising outcomes, such as the amelioration of the hierarchy problem and a natural candidate for dark matter. Nonetheless, the implications of embedding the Starobinsky model in a no-scale structure suggest a profound geometric interpretation, inexplicit in typical field-theoretic approaches. There is also an implicit suggestion of possible linkage with string-theoretic constructions, although such an association isn't mandatory for this particular framework.

Future Directions

While the authors propose a specific parameter set leading to successful results, analyzing this setup as a reference or groundwork could fuel further exploration into the landscape of inflationary models. Understanding and augmenting the superpotential beyond the minimal Wess-Zumino form and verifying how the indicated no-scale supergravity model could emerge from compactified string scenarios is potentially fruitful. Developing this line of inquiry might further provide insights into anomalies or variations observed in CMB data in the future, thus enriching our grasp of early Universe cosmology.

Conclusion

The discussed paper provides a rigorous foundation for a version of inflationary cosmology rooted in no-scale supergravity. The notable positioning of the model with respect to existing Planck data and its inherent theoretical implications place it as a significant paper offering a theoretical path to reconcile gravitational physics with quantum phenomena in cosmology. Continued attention in this direction might illuminate further intersections between high-energy physics models and observable cosmic phenomena.