Universality Class in Conformal Inflation (1306.5220v3)

Abstract: We develop a new class of chaotic inflation models with spontaneously broken conformal invariance. Observational consequences of a broad class of such models are stable with respect to strong deformations of the scalar potential. This universality is a critical phenomenon near the point of enhanced symmetry, SO(1,1), in case of conformal inflation. It appears because of the exponential stretching of the moduli space and the resulting exponential flattening of scalar potentials upon switching from the Jordan frame to the Einstein frame in this class of models. This result resembles stretching and flattening of inhomogeneities during inflationary expansion. It has a simple interpretation in terms of velocity versus rapidity near the Kahler cone in the moduli space, similar to the light cone of special theory of relativity. This effect makes inflation possible even in the models with very steep potentials. We describe conformal and superconformal versions of this cosmological attractor mechanism.

• The paper introduces a novel class of chaotic inflation models arising from spontaneously broken conformal invariance.
• It demonstrates that exponential stretching in the moduli space leads to universal attractor predictions, with nₛ and r matching observational data.
• It establishes a robust superconformal framework that reconciles theoretical models with key cosmic microwave background measurements.

Universality Class in Conformal Inflation

The paper by Renata Kallosh and Andrei Linde provides an in-depth analysis of a new class of chaotic inflation models that arise from spontaneously broken conformal invariance. The research introduces a theoretical framework that demonstrates the consistency and universality of these inflationary models when applied to observational data, particularly showcasing their stability against strong deformations of the scalar potential.

Overview of Main Contributions

The authors propose the extension of the superconformal approach to inflationary cosmology, suggesting that a broad category of inflationary models is contained within a universality class. This class is characterized by a scalar potential that experiences exponential flattening as a result of exponential stretching in the moduli space. The transformation from the Jordan to the Einstein frame within these models reveals this critical aspect of universality near an enhanced symmetry point, specifically $SO(1,1)$.

Key observational predictions, such as the spectral index $n_s$ and the tensor-to-scalar ratio $r$, consistently converge to $1 - n_{s} = 2/N$ and $r = 12/N^2$, respectively, in the leading $1/N$ approximation. This finding aligns with experimental data from cosmic microwave background observations like WMAP9 and Planck2013, highlighting the significance of this research in contributing to the larger discourse on the validation of inflationary scenarios.

Detailed Examination of Theoretical Framework

The paper explores a comprehensive formulation based on both conformal and superconformal symmetry. By utilizing scalar fields endowed with a local conformal symmetry, the authors reframe the traditional inflationary scenario into a structurally robust model. The potential $\lambda(\phi^2 - \chi^2)^2$ underlies these constructions, with $\chi$ serving as a 'conformon', a field aiding in the manifestation of local conformal symmetry.

Perturbations from symmetrical critical points are meticulously accounted for with the introduction of functions like $F(\phi/\chi)$, which preserves local conformal symmetry while allowing deformations. Such models, including the Starobinsky model variations, universally exhibit conformal and superconformal structures leading to the observed attractor behavior.

Implications and Future Directions

The implications of these findings are twofold: practically, this class of models provides a stable platform for further investigations into cosmological inflation with predictions resilient across various scenarios and perturbations. Theoretically, this research opens pathways to investigate further the symmetries inherent in conformal and superconformal theories, potentially unveiling new symmetry-breaking phenomena and their role in cosmological events.

The superconformal generalizations presented further enrich the theoretical landscape by integrating features such as moduli stabilization within a supersymmetric context, adhering to constraints observed in astrophysical data. Moreover, the demonstration of critical phenomena and the potential for establishing other attractor points in cosmological evolution positions this research as a cornerstone for future inquiries.

The universality of the results indicates robustness in their applicability, suggesting subsequent investigations might explore the integration of these models with string theory landscapes, or the implications on reheating and post-inflationary dynamics. This promising outlook presents opportunities for novel explorations into the connections binding symmetry principles to cosmic evolution narratives.

In conclusion, the paper may serve as a significant stepping stone towards a more unified and comprehensive understanding of inflationary dynamics through the lens of conformal symmetry, providing a foundation upon which future advances in theoretical cosmology may be constructed.