Journal of High Energy Physics

, 2013:134 | Cite as

On the supersymmetric completion of R + R 2 gravity and cosmology

  • Sergio Ferrara
  • Renata Kallosh
  • Antoine Van ProeyenEmail author
Open Access


We revisit and clarify the supersymmetric versions of R + R 2 gravity, in view of the renewed interest to these models in cosmology. We emphasize that the content of the dual standard supergravity theory in the old minimal formulation necessarily includes two massive chiral multiplets, that we call the inflaton and the goldstino. We point out that the presence of these multiplets is model independent in the old minimal formulation and therefore any theory that contains a single chiral multiplet fails to be a supersymmetric generalization of the R + R 2 gravity. The supergravity interactions of the two chiral multiplets are encoded in a superpotential mass term and an arbitrary Kähler potential for the goldstino multiplet. The implication for cosmology of the supersymmetric R + R 2 gravity is also discussed.


Supergravity Models Cosmology of Theories beyond the SM 


  1. [1]
    S. Ferrara, M.T. Grisaru and P. van Nieuwenhuizen, Poincaré and Conformal Supergravity Models With Closed Algebras, Nucl. Phys. B 138 (1978) 430 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S. Cecotti, Higher derivative supergravity is equivalent to standard supergravity coupled to matter. 1., Phys. Lett. B 190 (1987) 86 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    S. Cecotti, S. Ferrara, M. Porrati and S. Sabharwal, New minimal higher derivative supergravity coupled to matter, Nucl. Phys. B 306 (1988) 160 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    S. Ketov, F(R) supergravity, AIP Conf. Proc. 1241 (2010) 613 [arXiv:0910.1165] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    S.V. Ketov and A.A. Starobinsky, Embedding (R + R 2 )-Inflation into Supergravity, Phys. Rev. D 83 (2011) 063512 [arXiv:1011.0240] [INSPIRE].ADSGoogle Scholar
  6. [6]
    S.J. Gates Jr. and S.V. Ketov, Superstring-inspired supergravity as the universal source of inflation and quintessence, Phys. Lett. B 674 (2009) 59 [arXiv:0901.2467] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).CrossRefzbMATHGoogle Scholar
  8. [8]
    T. Kugo and S. Uehara, N = 1 Superconformal Tensor Calculus: Multiplets With External Lorentz Indices and Spinor Derivative Operators, Prog. Theor. Phys. 73 (1985) 235 [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
  9. [9]
    E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally Vanishing Cosmological Constant in N = 1 Supergravity, Phys. Lett. B 133 (1983) 61 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    J.R. Ellis, A. Lahanas, D.V. Nanopoulos and K. Tamvakis, No-Scale Supersymmetric Standard Model, Phys. Lett. B 134 (1984) 429 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    R. Kallosh and A. Linde, Superconformal generalizations of the Starobinsky model, JCAP 06 (2013) 028 [arXiv:1306.3214] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    R. Kallosh and A. Linde, Universality Class in Conformal Inflation, JCAP 07 (2013) 002 [arXiv:1306.5220] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    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].ADSCrossRefGoogle Scholar
  14. [14]
    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].ADSCrossRefGoogle Scholar
  15. [15]
    Y. Watanabe and J. Yokoyama, Gravitational modulated reheating and non-Gaussianity in Supergravity R 2 inflation, Phys. Rev. D 87 (2013) 103524 [arXiv:1303.5191] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA 2013

Authors and Affiliations

  • Sergio Ferrara
    • 1
    • 2
    • 5
  • Renata Kallosh
    • 3
  • Antoine Van Proeyen
    • 4
    Email author
  1. 1.Physics DepartmentTheory Unit, CERNGeneva 23Switzerland
  2. 2.INFN - Laboratori Nazionali di FrascatiFrascatiItaly
  3. 3.Stanford Institute for Theoretical Physics and Department of PhysicsStanford UniversityStanfordU.S.A.
  4. 4.Instituut voor Theoretische FysicaKU LeuvenLeuvenBelgium
  5. 5.Department of Physics and AstronomyUniversity of California Los AngelesLos AngelesU.S.A.

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