### Abstract

We study three types of the old-minimal higher-derivative supergravity theories extending the f (R) gravity, towards their use for the inflationary model building in supergravity, by using both superfields and their field components. In the curved superspace all those theories are described in terms of a single chiral scalar curvature superfeld R. Each of those theories can be dualized into a matter-coupled supergravity without higher derivatives. The first type is parametrized by a single non-holomorphic potential N (R, R̄), and gives rise to the dual matter-coupled supergravities with two dynamical chiral matter superfields having a no-scale Kähler potential. We find that a generic potential N (R, R̄) generates both the (R + R^{2}) gravity and the non-minimal coupling of the propagating complex scalar field to the R, needed for the Starobinsky and Higgs inflation, respectively. We find the general conditions for the Starobinsky inflation and compute the inflaton mass. The second type is given by the chiral supergravity actions whose superfield Lagrangian F (R, Σ(R̄)) also depends upon the chiral projection Σ of the anti-chiral superfield R̄. We find that the actions of the second type always give rise to ghosts. We also revisit the F (R) supergravity actions of the third type (without the Σ-dependence) with the reduced number of the extra physical degrees of freedom, comprising a single chiral matter superfeld with a no-scale Kähler potential. We confirm that the pure F (R) supergravity is insufficient for realization of the Starobinsky inflation, though by the reason different from those proposed in the recent literature.

Original language | English |
---|---|

Journal | Journal of High Energy Physics |

Volume | 2013 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cosmology of theories beyond the SM
- Supergravity models

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2013*(12). https://doi.org/10.1007/JHEP12(2013)040

**Old-minimal supergravity models of inflation.** / Ketov, Sergei V.; Terada, Takahiro.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2013, no. 12. https://doi.org/10.1007/JHEP12(2013)040

}

TY - JOUR

T1 - Old-minimal supergravity models of inflation

AU - Ketov, Sergei V.

AU - Terada, Takahiro

PY - 2013

Y1 - 2013

N2 - We study three types of the old-minimal higher-derivative supergravity theories extending the f (R) gravity, towards their use for the inflationary model building in supergravity, by using both superfields and their field components. In the curved superspace all those theories are described in terms of a single chiral scalar curvature superfeld R. Each of those theories can be dualized into a matter-coupled supergravity without higher derivatives. The first type is parametrized by a single non-holomorphic potential N (R, R̄), and gives rise to the dual matter-coupled supergravities with two dynamical chiral matter superfields having a no-scale Kähler potential. We find that a generic potential N (R, R̄) generates both the (R + R2) gravity and the non-minimal coupling of the propagating complex scalar field to the R, needed for the Starobinsky and Higgs inflation, respectively. We find the general conditions for the Starobinsky inflation and compute the inflaton mass. The second type is given by the chiral supergravity actions whose superfield Lagrangian F (R, Σ(R̄)) also depends upon the chiral projection Σ of the anti-chiral superfield R̄. We find that the actions of the second type always give rise to ghosts. We also revisit the F (R) supergravity actions of the third type (without the Σ-dependence) with the reduced number of the extra physical degrees of freedom, comprising a single chiral matter superfeld with a no-scale Kähler potential. We confirm that the pure F (R) supergravity is insufficient for realization of the Starobinsky inflation, though by the reason different from those proposed in the recent literature.

AB - We study three types of the old-minimal higher-derivative supergravity theories extending the f (R) gravity, towards their use for the inflationary model building in supergravity, by using both superfields and their field components. In the curved superspace all those theories are described in terms of a single chiral scalar curvature superfeld R. Each of those theories can be dualized into a matter-coupled supergravity without higher derivatives. The first type is parametrized by a single non-holomorphic potential N (R, R̄), and gives rise to the dual matter-coupled supergravities with two dynamical chiral matter superfields having a no-scale Kähler potential. We find that a generic potential N (R, R̄) generates both the (R + R2) gravity and the non-minimal coupling of the propagating complex scalar field to the R, needed for the Starobinsky and Higgs inflation, respectively. We find the general conditions for the Starobinsky inflation and compute the inflaton mass. The second type is given by the chiral supergravity actions whose superfield Lagrangian F (R, Σ(R̄)) also depends upon the chiral projection Σ of the anti-chiral superfield R̄. We find that the actions of the second type always give rise to ghosts. We also revisit the F (R) supergravity actions of the third type (without the Σ-dependence) with the reduced number of the extra physical degrees of freedom, comprising a single chiral matter superfeld with a no-scale Kähler potential. We confirm that the pure F (R) supergravity is insufficient for realization of the Starobinsky inflation, though by the reason different from those proposed in the recent literature.

KW - Cosmology of theories beyond the SM

KW - Supergravity models

UR - http://www.scopus.com/inward/record.url?scp=84896336327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896336327&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2013)040

DO - 10.1007/JHEP12(2013)040

M3 - Article

VL - 2013

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 12

ER -