Superconformal Inflationary $α$-Attractors

Abstract: Recently a broad class of superconformal inflationary models was found leading to a universal observational prediction $n_s=1-2/N$ and $r=12/N^2$. Here we generalize this class of models by introducing a parameter $\alpha$ inversely proportional to the curvature of the inflaton Kahler manifold. In the small curvature (large $\alpha$) limit, the observational predictions of this class of models coincide with the predictions of generic chaotic inflation models. However, for sufficiently large curvature (small $\alpha$), the predictions converge to the universal attractor regime with $n_s=1-2/N$ and $r=12\alpha/N^2$, which corresponds to the part of the $n_s-r$ plane favored by the Planck data.

• The paper introduces superconformal α-attractors that unify chaotic inflation models by modulating the inflaton manifold curvature with the parameter α to yield universal predictions for ns and r.
• The methodology employs a supergravity framework using both chiral superfields and vector multiplets to derive analytical results linking geometric curvature and inflationary observables.
• The research demonstrates that varying α produces a continuum of inflation models converging to attractor solutions that align closely with CMB data from observations like WMAP9 and Planck.

Superconformal Inflationary $\alpha$-Attractors

The paper "Superconformal Inflationary $\alpha$-Attractors" by Renata Kallosh, Andrei Linde, and Diederik Roest presents a comprehensive study of a broad class of inflationary models that incorporate superconformal symmetry. The authors introduce the concept of $\alpha$-attractors, a class of models that generalize previously discovered superconformal inflationary models and promise a universal attractor behavior for certain inflationary parameters. This paper elaborates on the implications of introducing a parameter $\alpha$, which modulates the curvature of the inflaton manifold and affects the model's predictions for observable inflationary parameters such as the spectral index $n_s$ and the tensor-to-scalar ratio $r$.

Conceptual Framework and Model Development

The motivation behind this work arises from the challenges faced in realizing generic chaotic inflation models within the field of supergravity. Previous progress had allowed the realization of chaotic inflation models in supergravity with various potentials and matter multiplets, laying the groundwork for the investigation of models that align closely with observational data.

The main focus of this paper is on models leading to observational predictions that interpolate from generic chaotic inflation behaviors to a universal attractor regime defined by $n_s = 1 - \frac{2}{N}$ and $r = \alpha \frac{12}{N^2}$, where $N$ is the number of e-folds. The parameter $\alpha$ is inversely related to the curvature of the inflaton's scalar manifold, denoted as $R_K = -\frac{2}{3\alpha}$. This relationship endows the parameter $\alpha$ with a geometrical interpretation as a curvature regulator.

Analytical Approach and Observational Implications

Incorporating the parameter $\alpha$ provides a continuum of models ranging from the large $N$ limit of chaotic inflation scenarios to a universal attractor scenario. For large values of $\alpha$, the models tend to predict observational outcomes consistent with chaotic inflation—specifically those with monomial potentials. However, as the curvature's influence increases (i.e., for smaller $\alpha$), the observational predictions converge to the attractor values favored by contemporary cosmic microwave background (CMB) data such as those from WMAP9 and Planck 2013.

The paper explores two major classes of models: one built on vector multiplets and another on chiral superfields. Both serve to reinforce the role of supergravity as an encompassing framework where these $\alpha$-attractors can be realized.

Results and Theoretical Impact

The predicted range of observable parameters, especially the spectral index $n_s$ and the tensor-to-scalar ratio $r$, continuously interpolate between the values dictated by typical chaotic inflation models and those of the universal attractor. The analytical results derived in the research confirm the attractor nature of these models, which suggests that a wide variety of initial inflationary scenarios can end up with similar observable traits at the CMB scale.

The implications of this research extend to both practical observational testability and theoretical advances in the study of the early universe. By delineating a rich spectrum of potential inflation models accommodated within supergravity, this paper allows for a deeper exploration into the interplay between particle physics and cosmology.

Conclusion and Future Directions

The exploration of $\alpha$-attractors as conducted in this study broadens the scope of supergravity models capable of explaining cosmological inflation. Future work may explore additional constraints on $\alpha$ to refine predictions further and verify compatibility with more precise data. These findings stimulate further investigation into superconformal symmetries and the potential they hold to elucidate hidden dynamics in the inflationary epoch, potentially making $\alpha$-attractors a focal point in the endeavor to reconcile theoretical cosmology with empirical observation.