Abstract
Recently a broad class of superconformal inflationary models was found leading to a universal observational prediction \( {n_s}=1-\frac{2}{N} \) and \( r=\frac{12 }{{{N^2}}} \) [1, 2]. Here we generalize this class of models by introducing a parameter α inversely proportional to the curvature of the inflaton Kähler manifold. In the small curvature (large α) limit, the observational predictions of this class of models coincide with the predictions of generic chaotic inflation models. However, for sufficiently large curvature (small α), the predictions converge to the universal attractor regime with \( {n_s}=1-\frac{2}{N} \) and \( r=\alpha \frac{12 }{{{N^2}}} \), which corresponds to the part of the n s − r plane favored by the Planck data.
Similar content being viewed by others
References
R. Kallosh and A. Linde, Universality class in conformal inflation, JCAP 07 (2013) 002 [arXiv:1306.5220] [INSPIRE].
R. Kallosh and A. Linde, Multi-field Conformal Cosmological Attractors, arXiv:1309.2015 [INSPIRE].
A.D. Linde, Chaotic inflation, Phys. Lett. B 129 (1983) 177 [INSPIRE].
M. Kawasaki, M. Yamaguchi and T. Yanagida, Natural chaotic inflation in supergravity, Phys. Rev. Lett. 85 (2000) 3572 [hep-ph/0004243] [INSPIRE].
R. Kallosh and A. Linde, New models of chaotic inflation in supergravity, JCAP 11 (2010) 011 [arXiv:1008.3375] [INSPIRE].
R. Kallosh, A. Linde and T. Rube, General inflaton potentials in supergravity, Phys. Rev. D 83 (2011) 043507 [arXiv:1011.5945] [INSPIRE].
S. Ferrara, R. Kallosh, A. Linde and M. Porrati, Minimal Supergravity Models of Inflation, arXiv:1307.7696 [INSPIRE].
R. Kallosh and A. Linde, Superconformal generalization of the chaotic inflation model \( \frac{\lambda }{4}{\phi^4}-\frac{\xi }{2}{\phi^2}R \), JCAP 06 (2013) 027 [arXiv:1306.3211] [INSPIRE].
R. Kallosh and A. Linde, Superconformal generalizations of the Starobinsky model, JCAP 06 (2013) 028 [arXiv:1306.3214] [INSPIRE].
R. Kallosh and A. Linde, Non-minimal inflationary attractors, JCAP 10 (2013) 033 [arXiv:1307.7938] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, A universal attractor for inflation at strong coupling, arXiv:1310.3950 [INSPIRE].
WMAP collaboration, G. Hinshaw et al., Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results, Astrophys. J. Suppl. 208 (2013) 19 [arXiv:1212.5226] [INSPIRE].
Planck collaboration, P. Ade et al., Planck 2013 results. XXII. Constraints on inflation, arXiv:1303.5082 [INSPIRE].
Planck collaboration, P. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
V.F. Mukhanov and G.V. Chibisov, Quantum Fluctuation and Nonsingular Universe (in Russian), JETP Lett. 33 (1981) 532 [Pisma Zh. Eksp. Teor. Fiz. 33 (1981) 549] [INSPIRE].
A.A. Starobinsky, The Perturbation Spectrum Evolving from a Nonsingular Initially De-Sitte r Cosmology and the Microwave Background Anisotropy, Sov. Astron. Lett. 9 (1983) 302 [INSPIRE].
D. Salopek, J. Bond and J.M. Bardeen, Designing density fluctuation spectra in inflation, Phys. Rev. D 40 (1989) 1753 [INSPIRE].
F.L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703 [arXiv:0710.3755] [INSPIRE].
N. Okada, M.U. Rehman and Q. Shafi, Tensor to Scalar Ratio in Non-Minimal ϕ 4 Inflation, Phys. Rev. D 82 (2010) 043502 [arXiv:1005.5161] [INSPIRE].
F. Bezrukov and D. Gorbunov, Light inflaton after LHC8 and WMAP9 results, JHEP 07 (2013) 140 [arXiv:1303.4395] [INSPIRE].
A. Linde, M. Noorbala and A. Westphal, Observational consequences of chaotic inflation with nonminimal coupling to gravity, JCAP 03 (2011) 013 [arXiv:1101.2652] [INSPIRE].
D.I. Kaiser and E.I. Sfakianakis, Multifield Inflation after Planck: The Case for Nonminimal Couplings, arXiv:1304.0363 [INSPIRE].
J. Ellis, D.V. Nanopoulos and K.A. Olive, No-Scale Supergravity Realization of the Starobinsky Model of Inflation, Phys. Rev. Lett. 111 (2013) 111301 [arXiv:1305.1247] [INSPIRE].
J. Ellis, D.V. Nanopoulos and K.A. Olive, Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity, JCAP 10 (2013) 009 [arXiv:1307.3537] [INSPIRE].
W. Buchmüller, V. Domcke and K. Kamada, The Starobinsky Model from Superconformal D-Term Inflation, Phys. Lett. B 726 (2013) 467 [arXiv:1306.3471] [INSPIRE].
A. Goncharov and A.D. Linde, Chaotic inflation in supergravity, Phys. Lett. B 139 (1984) 27 [INSPIRE].
V. Mukhanov, Quantum Cosmological Perturbations: Predictions and Observations, Eur. Phys. J. C 73 (2013) 2486 [arXiv:1303.3925] [INSPIRE].
D. Roest, Universality classes of inflation, arXiv:1309.1285 [INSPIRE].
B. Whitt, Fourth Order Gravity as General Relativity Plus Matter, Phys. Lett. B 145 (1984) 176 [INSPIRE].
D. Roest, M. Scalisi and I. Zavala, Kähler potentials for Planck inflation, JCAP 11 (2013) 007 [arXiv:1307.4343] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1311.0472
Rights and permissions
About this article
Cite this article
Kallosh, R., Linde, A. & Roest, D. Superconformal inflationary α-attractors. J. High Energ. Phys. 2013, 198 (2013). https://doi.org/10.1007/JHEP11(2013)198
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2013)198