Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity (1307.3537v1)

Abstract: Models of cosmological inflation resembling the Starobinsky R + R^2 model emerge naturally among the effective potentials derived from no-scale SU(N,1)/SU(N) x U(1) supergravity when N > 1. We display several examples in the SU(2,1)/SU(2) x U(1) case, in which the inflaton may be identified with either a modulus field or a matter field. We discuss how the modulus field may be stabilized in models in which a matter field plays the role of the inflaton. We also discuss models that generalize the Starobinsky model but display different relations between the tilt in the spectrum of scalar density perturbations, n_s, the tensor-to-scalar ratio, r, and the number of e-folds, N_*. Finally, we discuss how such models can be probed by present and future CMB experiments.

• The paper demonstrates that no-scale supergravity frameworks can naturally generate Starobinsky-like inflationary potentials that align with CMB constraints.
• The methodology employs tailored superpotential and Kähler potential configurations to stabilize the modulus via matter field dynamics.
• The models predict a spectral index nₛ ≈ 0.96 and a tensor-to-scalar ratio r ≈ 0.004, offering testable implications for CMB observations.

Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity

The paper under review ventures into an exploration of inflationary cosmology within the framework of no-scale supergravity, motivated by the constraints imposed by contemporary Cosmic Microwave Background (CMB) observations, notably those from the Planck satellite. This research elaborates on models resembling the Starobinsky $R + R^2$ model and situates them within the theoretical construct of no-scale SU(N,1)/SU(N) $\times$ U(1) supergravity, particularly for cases where $N > 1$.

At the heart of the analysis is the intersection of two compelling theoretical avenues: the Starobinsky's $R + R^2$ gravity framework and no-scale supergravity. The Starobinsky model, admired for its concordance with CMB observations through a spectral index $n_s \sim 0.96$ and tensor-to-scalar ratio $r \sim 0.004$, serves as an archetype with predictions closely aligning with observed data. Universally appealing is its potential connection to phenomena like supersymmetry breaking and consistency with scalar field dynamics originating at energy scales hierarchically below the Planck scale, hinting at an underlying supersymmetric mechanism.

The authors put forward the intriguing notion of no-scale supergravity as a fertile ground for naturally reproducing Starobinsky-like inflationary dynamics. Notably, they underline the capacity of the SU(2,1)/SU(2) $\times$ U(1) model, among others, to support such claims where either a modulus or a matter field assumes the role of the inflaton. A key insight is the demonstration of the possibility to stabilize the modulus field through the dynamics of an inflating matter field. The paper is replete with examples illustrating these configurations, meticulously highlighting how variations in the superpotential parameter space can yield the canonical Starobinsky potential or modify it within experimentally permissible bounds.

In addressing the broader applicability and potential implications of these models, the paper considers the ramifications for CMB experiments. The models' predictions, especially with regard to the tensor-to-scalar ratio and scalar spectral index, are positioned as within reach of current and forthcoming experimental capabilities, thereby setting a critical test for the validity and utility of these theoretical frameworks. For the field, these models not only pose the potential to delineate the nature of the inflaton but also provide a possible window into the structure of the underlying supergravity fields.

Furthermore, the discussion extends to the stabilization of the modulus field within these frameworks—a significant consideration given the challenges in realizing realistic inflationary dynamics. The research provides explicit strategies for achieving such stabilization, underscoring its feasibility within the described theoretical setting.

In summary, this paper presents a sophisticated examination of inflationary scenarios in a no-scale supergravity context, demonstrating both the theoretical robustness and the observational viability of these models as a continuation or generalization of the Starobinsky paradigm. Its implications for future research involve a rigorous exploration of the role of different superpotential configurations and Kähler potentials, and possibly, offering insights into supergravity’s contribution to our understanding of early universe cosmology. As experimental benchmarks evolve, the predictions of these models will either reinforce the direction laid herein or carve new inquiries necessitating further theoretical innovation.