Abstract
Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The Kähler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and gravitino mass. We illustrate it by providing generalized versions of polynomial chaotic inflation, T- and E-models of α-attractor type, disk merger. We also describe a multi-stage cosmological attractor regime, which we call cascade inflation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister and S.P. Trivedi, Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].
D.V. Volkov and V.P. Akulov, Possible universal neutrino interaction, JETP Lett. 16 (1972) 438 [Pisma Zh. Eksp. Teor. Fiz. 16 (1972) 621] [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
M. Roček, Linearizing the Volkov-Akulov model, Phys. Rev. Lett. 41 (1978) 451 [INSPIRE].
E.A. Ivanov and A.A. Kapustnikov, General relationship between linear and nonlinear realizations of supersymmetry, J. Phys. A 11 (1978) 2375 [INSPIRE].
U. Lindstrom and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].
R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto, Nonlinear realization of supersymmetry algebra from supersymmetric constraint, Phys. Lett. B 220 (1989) 569 [INSPIRE].
Z. Komargodski and N. Seiberg, From linear SUSY to constrained superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Relating the Komargodski-Seiberg and Akulov-Volkov actions: exact nonlinear field redefinition, Phys. Lett. B 698 (2011) 319 [arXiv:1009.3298] [INSPIRE].
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].
G. Dall’Agata and F. Farakos, Constrained superfields in supergravity, JHEP 02 (2016) 101 [arXiv:1512.02158] [INSPIRE].
S. Ferrara, R. Kallosh, A. Van Proeyen and T. Wrase, Linear versus non-linear supersymmetry, in general, JHEP 04 (2016) 065 [arXiv:1603.02653] [INSPIRE].
R. Kallosh, A. Karlsson, B. Mosk and D. Murli, Orthogonal nilpotent superfields from linear models, JHEP 05 (2016) 082 [arXiv:1603.02661] [INSPIRE].
G. Dall’Agata, E. Dudas and F. Farakos, On the origin of constrained superfields, JHEP 05 (2016) 041 [arXiv:1603.03416] [INSPIRE].
R. Kallosh and T. Wrase, Emergence of spontaneously broken supersymmetry on an anti-D3-brane in KKLT dS vacua, JHEP 12 (2014) 117 [arXiv:1411.1121] [INSPIRE].
E.A. Bergshoeff, K. Dasgupta, R. Kallosh, A. Van Proeyen and T. Wrase, \( \overline{D3} \) and dS, JHEP 05 (2015) 058 [arXiv:1502.07627] [INSPIRE].
R. Kallosh, F. Quevedo and A.M. Uranga, String theory realizations of the nilpotent goldstino, JHEP 12 (2015) 039 [arXiv:1507.07556] [INSPIRE].
L. Aparicio, F. Quevedo and R. Valandro, Moduli stabilisation with nilpotent goldstino: vacuum structure and SUSY breaking, JHEP 03 (2016) 036 [arXiv:1511.08105] [INSPIRE].
I. García-Etxebarria, F. Quevedo and R. Valandro, Global string embeddings for the nilpotent goldstino, JHEP 02 (2016) 148 [arXiv:1512.06926] [INSPIRE].
K. Dasgupta, M. Emelin and E. McDonough, Fermions on the antibrane: higher order interactions and spontaneously broken supersymmetry, Phys. Rev. D 95 (2017) 026003 [arXiv:1601.03409] [INSPIRE].
B. Vercnocke and T. Wrase, Constrained superfields from an anti-D3-brane in KKLT, JHEP 08 (2016) 132 [arXiv:1605.03961] [INSPIRE].
R. Kallosh, B. Vercnocke and T. Wrase, String theory origin of constrained multiplets, JHEP 09 (2016) 063 [arXiv:1606.09245] [INSPIRE].
I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov-Akulov-Starobinsky supergravity, Phys. Lett. B 733 (2014) 32 [arXiv:1403.3269] [INSPIRE].
S. Ferrara, R. Kallosh and A. Linde, Cosmology with nilpotent superfields, JHEP 10 (2014) 143 [arXiv:1408.4096] [INSPIRE].
R. Kallosh and A. Linde, Inflation and uplifting with nilpotent superfields, JCAP 01 (2015) 025 [arXiv:1408.5950] [INSPIRE].
G. Dall’Agata and F. Zwirner, On sgoldstino-less supergravity models of inflation, JHEP 12 (2014) 172 [arXiv:1411.2605] [INSPIRE].
R. Kallosh, A. Linde and M. Scalisi, Inflation, de Sitter landscape and super-Higgs effect, JHEP 03 (2015) 111 [arXiv:1411.5671] [INSPIRE].
E. Cremmer, B. Julia, J. Scherk, P. van Nieuwenhuizen, S. Ferrara and L. Girardello, Super-Higgs effect in supergravity with general scalar interactions, Phys. Lett. B 79 (1978) 231 [INSPIRE].
E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect, Nucl. Phys. B 212 (1983) 413 [INSPIRE].
P. Binetruy and G.R. Dvali, D term inflation, Phys. Lett. B 388 (1996) 241 [hep-ph/9606342] [INSPIRE].
R. Kallosh, A. Linde and T. Rube, General inflaton potentials in supergravity, Phys. Rev. D 83 (2011) 043507 [arXiv:1011.5945] [INSPIRE].
M. Gomez-Reino and C.A. Scrucca, Locally stable non-supersymmetric Minkowski vacua in supergravity, JHEP 05 (2006) 015 [hep-th/0602246] [INSPIRE].
A. Achucarro and K. Sousa, F-term uplifting and moduli stabilization consistent with Kähler invariance, JHEP 03 (2008) 002 [arXiv:0712.3460] [INSPIRE].
L. Covi, M. Gomez-Reino, C. Gross, J. Louis, G.A. Palma and C.A. Scrucca, Constraints on modular inflation in supergravity and string theory, JHEP 08 (2008) 055 [arXiv:0805.3290] [INSPIRE].
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].
K. Sousa and P. Ortiz, Perturbative stability along the supersymmetric directions of the landscape, JCAP 02 (2015) 017 [arXiv:1408.6521] [INSPIRE].
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].
J.J.M. Carrasco, R. Kallosh and A. Linde, α-attractors: Planck, LHC and dark energy, JHEP 10 (2015) 147 [arXiv:1506.01708] [INSPIRE].
E. McDonough and M. Scalisi, Inflation from nilpotent Kähler corrections, JCAP 11 (2016) 028 [arXiv:1609.00364] [INSPIRE].
R. Kallosh and T. Wrase, De Sitter supergravity model building, Phys. Rev. D 92 (2015) 105010 [arXiv:1509.02137] [INSPIRE].
M. Schillo, E. van der Woerd and T. Wrase, The general de Sitter supergravity component action, Fortsch. Phys. 64 (2016) 292 [arXiv:1511.01542] [INSPIRE].
S. Ferrara and A. Van Proeyen, Mass formulae for broken supersymmetry in curved space-time, Fortsch. Phys. 64 (2016) 896 [arXiv:1609.08480] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
C. Destri, H.J. de Vega and N.G. Sanchez, MCMC analysis of WMAP3 and SDSS data points to broken symmetry inflaton potentials and provides a lower bound on the tensor to scalar ratio, Phys. Rev. D 77 (2008) 043509 [astro-ph/0703417] [INSPIRE].
K. Nakayama, F. Takahashi and T.T. Yanagida, Polynomial chaotic inflation in the Planck era, Phys. Lett. B 725 (2013) 111 [arXiv:1303.7315] [INSPIRE].
K. Nakayama, F. Takahashi and T.T. Yanagida, Polynomial chaotic inflation in supergravity, JCAP 08 (2013) 038 [arXiv:1305.5099] [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 A. Westphal, Chaotic inflation in supergravity after Planck and BICEP2, Phys. Rev. D 90 (2014) 023534 [arXiv:1405.0270] [INSPIRE].
A.D. Linde, Particle physics and inflationary cosmology, Contemp. Concepts Phys. 5 (1990) 1 [hep-th/0503203] [INSPIRE].
A. Linde, Inflationary cosmology after Planck 2013, in Proceedings, 100th Les Houches Summer School: post-Planck Cosmology , Les Houches France, 8 July-2 August 2013 [arXiv:1402.0526] [INSPIRE].
R. Kallosh, A. Linde, T. Wrase and Y. Yamada, Maximal supersymmetry and B-mode targets, JHEP 04 (2017) 144 [arXiv:1704.04829] [INSPIRE].
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].
W.E. East, M. Kleban, A. Linde and L. Senatore, Beginning inflation in an inhomogeneous universe, JCAP 09 (2016) 010 [arXiv:1511.05143] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1705.09247
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Kallosh, R., Linde, A., Roest, D. et al. \( \overline{D3} \) induced geometric inflation. J. High Energ. Phys. 2017, 57 (2017). https://doi.org/10.1007/JHEP07(2017)057
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2017)057