Coupling the inflationary sector to matter

Open Access
Regular Article - Theoretical Physics


We describe the coupling of matter fields to an inflationary sector of supergravity, the inflaton Φ and a stabilizer S, in models where the Kähler potential has a flat inflaton direction. Such models include, in particular, advanced versions of the hyperbolic α-attractor models with a flat inflaton direction Kähler potential, providing a good fit to the observational data. If the superpotential is at least quadratic in the matter fields U i , with restricted couplings to the inflaton sector, we prove that under certain conditions: i) The presence of the matter fields does not affect a successful inflationary evolution. ii) There are no tachyons in the matter sector during and after inflation. iii) The matter masses squared are higher than 3H 2 during inflation. The simplest class of theories satisfying all required conditions is provided by models with a flat direction Kähler potential, and with the inflaton Φ and a stabilizer S belonging to a hidden sector, so that matter fields have no direct coupling to the inflationary sector in the Kähler potential and in the superpotential.


Supergravity Models Cosmology of Theories beyond the SM 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    M. Kawasaki, M. Yamaguchi and T. Yanagida, Natural chaotic inflation in supergravity, Phys. Rev. Lett. 85 (2000) 3572 [hep-ph/0004243] [INSPIRE].
  2. [2]
    R. Kallosh and A. Linde, New models of chaotic inflation in supergravity, JCAP 11 (2010) 011 [arXiv:1008.3375] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    R. Kallosh, A. Linde and T. Rube, General inflaton potentials in supergravity, Phys. Rev. D 83 (2011) 043507 [arXiv:1011.5945] [INSPIRE].ADSGoogle Scholar
  4. [4]
    A.S. Goncharov and A.D. Linde, Chaotic inflation of the universe in supergravity, Sov. Phys. JETP 59 (1984) 930 [INSPIRE].Google Scholar
  5. [5]
    A.B. Goncharov and A.D. Linde, Chaotic Inflation in Supergravity, Phys. Lett. B 139 (1984) 27 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    A. Linde, Does the first chaotic inflation model in supergravity provide the best fit to the Planck data?, JCAP 02 (2015) 030 [arXiv:1412.7111] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    R. Kallosh and A. Linde, Universality Class in Conformal Inflation, JCAP 07 (2013) 002 [arXiv:1306.5220] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Ferrara, R. Kallosh, A. Linde and M. Porrati, Minimal Supergravity Models of Inflation, Phys. Rev. D 88 (2013) 085038 [arXiv:1307.7696] [INSPIRE].ADSGoogle Scholar
  9. [9]
    R. Kallosh, A. Linde and D. Roest, Superconformal Inflationary α-Attractors, JHEP 11 (2013) 198 [arXiv:1311.0472] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    J.J.M. Carrasco, R. Kallosh, A. Linde and D. Roest, Hyperbolic geometry of cosmological attractors, Phys. Rev. D 92 (2015) 041301 [arXiv:1504.05557] [INSPIRE].ADSGoogle Scholar
  11. [11]
    J.J.M. Carrasco, R. Kallosh and A. Linde, Cosmological Attractors and Initial Conditions for Inflation, Phys. Rev. D 92 (2015) 063519 [arXiv:1506.00936] [INSPIRE].ADSGoogle Scholar
  12. [12]
    J.J.M. Carrasco, R. Kallosh and A. Linde, α-Attractors: Planck, LHC and Dark Energy, JHEP 10 (2015) 147 [arXiv:1506.01708] [INSPIRE].
  13. [13]
    R. Kallosh and A. Linde, Escher in the Sky, Comptes Rendus Physique 16 (2015) 914 [arXiv:1503.06785] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, arXiv:1502.02114 [INSPIRE].
  15. [15]
    BICEP2, Keck Array collaborations, P.A.R. Ade et al., Improved Constraints on Cosmology and Foregrounds from BICEP2 and Keck Array Cosmic Microwave Background Data with Inclusion of 95 GHz Band, Phys. Rev. Lett. 116 (2016) 031302 [arXiv:1510.09217] [INSPIRE].
  16. [16]
    Planck collaboration, P.A.R. Ade et al., Planck intermediate results. XLI. A map of lensing-induced B-modes, arXiv:1512.02882 [INSPIRE].
  17. [17]
    W.E. East, M. Kleban, A. Linde and L. Senatore, Beginning inflation in an inhomogeneous universe, arXiv:1511.05143 [INSPIRE].
  18. [18]
    A. Brignole, F. Feruglio and F. Zwirner, On the effective interactions of a light gravitino with matter fermions, JHEP 11 (1997) 001 [hep-th/9709111] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    Z. Komargodski and N. Seiberg, From Linear SUSY to Constrained Superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    Y. Kahn, D.A. Roberts and J. Thaler, The goldstone and goldstino of supersymmetric inflation, JHEP 10 (2015) 001 [arXiv:1504.05958] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    G. Dall’Agata, S. Ferrara and F. Zwirner, Minimal scalar-less matter-coupled supergravity, Phys. Lett. B 752 (2016) 263 [arXiv:1509.06345] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    S. Ferrara, R. Kallosh and J. Thaler, Cosmology with orthogonal nilpotent superfields, Phys. Rev. D 93 (2016) 043516 [arXiv:1512.00545] [INSPIRE].ADSGoogle Scholar
  23. [23]
    J.J.M. Carrasco, R. Kallosh and A. Linde, Inflatino-less Cosmology, Phys. Rev. D 93 (2016) 061301 [arXiv:1512.00546] [INSPIRE].Google Scholar
  24. [24]
    G. Dall’Agata and F. Farakos, Constrained superfields in Supergravity, JHEP 02 (2016) 101 [arXiv:1512.02158] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    A. Achucarro, S. Hardeman, J.M. Oberreuter, K. Schalm and T. van der Aalst, Decoupling limits in multi-sector supergravities, JCAP 03 (2013) 038 [arXiv:1108.2278] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    R. Kallosh, A. Linde and A. Westphal, Chaotic Inflation in Supergravity after Planck and BICEP2, Phys. Rev. D 90 (2014) 023534 [arXiv:1405.0270] [INSPIRE].ADSGoogle Scholar
  27. [27]
    G. Dall’Agata and F. Zwirner, On sgoldstino-less supergravity models of inflation, JHEP 12 (2014) 172 [arXiv:1411.2605] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    R. Kallosh, A. Karlsson and D. Murli, From linear to nonlinear supersymmetry via functional integration, Phys. Rev. D 93 (2016) 025012 [arXiv:1511.07547] [INSPIRE].ADSGoogle Scholar
  29. [29]
    R. Kallosh, A. Karlsson, B. Mosk and D. Murli, Orthogonal Nilpotent Superfields from Linear Models, arXiv:1603.02661 [INSPIRE].
  30. [30]
    E. Dudas, L. Heurtier, C. Wieck and M.W. Winkler, UV Corrections in Sgoldstino-less Inflation, arXiv:1601.03397 [INSPIRE].
  31. [31]
    R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press (1990).Google Scholar
  32. [32]
    J.R. Ellis, A.D. Linde and D.V. Nanopoulos, Inflation Can Save the Gravitino, Phys. Lett. B 118 (1982) 59 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    D.V. Nanopoulos, K.A. Olive and M. Srednicki, After Primordial Inflation, Phys. Lett. B 127 (1983) 30 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    M. Yu. Khlopov and A.D. Linde, Is It Easy to Save the Gravitino?, Phys. Lett. B 138 (1984) 265 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    T. Moroi, Effects of the gravitino on the inflationary universe, hep-ph/9503210 [INSPIRE].
  36. [36]
    R. Kallosh, A. Linde, D. Roest and T. Wrase, in preparation.Google Scholar
  37. [37]
    A.D. Linde, Axions in inflationary cosmology, Phys. Lett. B 259 (1991) 38 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    A.D. Linde, Hybrid inflation, Phys. Rev. D 49 (1994) 748 [astro-ph/9307002] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.SITP and Department of PhysicsStanford UniversityStanfordU.S.A.
  2. 2.Institute for Theoretical Physics, TU WienViennaAustria

Personalised recommendations