Abstract
We consider a broad class of inflationary models that arise naturally in super-gravity. They are defined in terms of a parameter α that determines the curvature and cutoff of these models. As a function of this parameter, we exhibit that the inflationary predictions generically interpolate between two attractor points. At small cutoff α, the resulting inflationary model is of plateau-type with n s = 1 − 2/N and r = 12α/N 2. For α = 1, these predictions coincide with predictions of the Starobinsky model and Higgs inflation. In contrast, for large cutoff α, the theory asymptotes to quadratic inflation, with n s = 1 − 2/N, r = 8/N. Both universal predictions can be attributed to a stretching of the moduli space. For intermediate values of α, the predictions interpolate between these two critical points, thus covering the sweet spots of both Planck and BICEP2.
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References
A.D. Linde, Chaotic Inflation, Phys. Lett. B 129 (1983) 177 [INSPIRE].
A.D. Linde, Particle physics and inflationary cosmology, Contemp. Concepts Phys. 5 (1990) 1 [hep-th/0503203] [INSPIRE].
A.D. Linde, Inflationary Cosmology, Lect. Notes Phys. 738 (2008) 1 [arXiv:0705.0164] [INSPIRE].
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo - Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].
R. Kallosh, A. Linde and B. Vercnocke, Natural Inflation in Supergravity and Beyond, arXiv:1404.6244 [INSPIRE].
E. Silverstein and A. Westphal, Monodromy in the CMB: Gravity Waves and String Inflation, Phys. Rev. D 78 (2008) 106003 [arXiv:0803.3085] [INSPIRE].
L. McAllister, E. Silverstein and A. Westphal, Gravity Waves and Linear Inflation from Axion Monodromy, Phys. Rev. D 82 (2010) 046003 [arXiv:0808.0706] [INSPIRE].
BICEP2 collaboration, P.A.R. Ade et al., Detection of B-Mode Polarization at Degree Angular Scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, arXiv:1303.5082 [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [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].
B. Whitt, Fourth Order Gravity as General Relativity Plus Matter, Phys. Lett. B 145 (1984) 176 [INSPIRE].
L.A. Kofman, A.D. Linde and A.A. Starobinsky, Inflationary Universe Generated by the Combined Action of a Scalar Field and Gravitational Vacuum Polarization, Phys. Lett. B 157 (1985) 361 [INSPIRE].
D.S. Salopek, J.R. 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].
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, JCAP 12 (2013) 006 [arXiv:1309.2015] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, Universal Attractor for Inflation at Strong Coupling, Phys. Rev. Lett. 112 (2014) 011303 [arXiv:1310.3950] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, Superconformal Inflationary α-Attractors, JHEP 11 (2013) 198 [arXiv:1311.0472] [INSPIRE].
A.D. Linde, Inflation and quantum Cosmology, in 300 Years of Gravitation, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge (1987).
R. Kallosh and A. Linde, Hidden Superconformal Symmetry of the Cosmological Evolution, JCAP 01 (2014) 020 [arXiv:1311.3326] [INSPIRE].
J.J.M. Carrasco, W. Chemissany and R. Kallosh, Journeys Through Antigravity?, JHEP 01 (2014) 130 [arXiv:1311.3671] [INSPIRE].
A. Linde, Inflationary Cosmology after Planck 2013, arXiv:1402.0526 [INSPIRE].
Y.-F. Cai, J.-O. Gong and S. Pi, Conformal description of inflation and primordial B-modes, arXiv:1404.2560 [INSPIRE].
S. Ferrara, R. Kallosh, A. Linde and M. Porrati, Minimal Supergravity Models of Inflation, Phys. Rev. D 88 (2013) 085038 [arXiv:1307.7696] [INSPIRE].
D. Roest, Universality classes of inflation, JCAP 01 (2014) 007 [arXiv:1309.1285] [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].
A. Ceresole, G. Dall’Agata, S. Ferrara, M. Trigiante and A. Van Proeyen, A search for an \( \mathcal{N} \) =2 inflaton potential, Fortsch. Phys. 62 (2014) 584 [arXiv:1404.1745] [INSPIRE].
S.V. Ketov, Starobinsky Model in N = 2 Supergravity, Phys. Rev. D 89 (2014) 085042 [arXiv:1402.0626] [INSPIRE].
S. Cecotti and R. Kallosh, Cosmological Attractor Models and Higher Curvature Supergravity, JHEP 05 (2014) 114 [arXiv:1403.2932] [INSPIRE].
S. Cecotti, Higher derivative supergravity is equivalent to standard supergravity coupled to matter. 1., Phys. Lett. B 190 (1987) 86 [INSPIRE].
D. Roest, M. Scalisi and I. Zavala, Kähler potentials for Planck inflation, JCAP 11 (2013) 007 [arXiv:1307.4343] [INSPIRE].
D.H. Lyth, BICEP2, the curvature perturbation and supersymmetry, arXiv:1403.7323 [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].
R. Kallosh, A. Linde and A. Westphal, Chaotic Inflation in Supergravity after Planck and BICEP2, arXiv:1405.0270 [INSPIRE].
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Kallosh, R., Linde, A. & Roest, D. Large field inflation and double α-attractors. J. High Energ. Phys. 2014, 52 (2014). https://doi.org/10.1007/JHEP08(2014)052
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DOI: https://doi.org/10.1007/JHEP08(2014)052