Abstract
We investigate effects of the radiation and the moduli oscillation around the stabilized values on the evolution of a 6-dimensional spacetime compactified on S2. In order to see the transition from the 5-dimensional space to the 3-dimensional one, we develop a procedure to pursue the spacetime evolution with appropriate approximations, which is valid until the spacetime behaves like 4-dimensional. In the case that the moduli stabilization process cannot be described in the context of the 4-dimensional effective theory, it takes quite a long time for the moduli oscillation to dominate the total energy density, in contrast to the conventional result obtained by the 4-dimensional effective theory approach. We also found that even if the moduli are set at the stabilized values, they start to oscillate due to the pressure in the extra space S2 in some cases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Salam and E. Sezgin, Chiral Compactification on Minkowski ×S2 of N = 2 Einstein-Maxwell Supergravity in Six-Dimensions, Phys. Lett. B 147 (1984) 47 [INSPIRE].
H. Nishino and E. Sezgin, Matter and Gauge Couplings of N = 2 Supergravity in Six-Dimensions, Phys. Lett. B 144 (1984) 187 [INSPIRE].
S. Randjbar-Daemi, A. Salam, E. Sezgin and J.A. Strathdee, An Anomaly Free Model in Six-Dimensions, Phys. Lett. B 151 (1985) 351 [INSPIRE].
K.-I. Maeda and H. Nishino, Cosmological Solutions in D = 6, N = 2 Kaluza-Klein Supergravity: Friedmann Universe Without Fine Tuning, Phys. Lett. B 154 (1985) 358 [INSPIRE].
M.B. Green, J.H. Schwarz and P.C. West, Anomaly Free Chiral Theories in Six-Dimensions, Nucl. Phys. B 254 (1985) 327 [INSPIRE].
G.D. Coughlan et al., Cosmological Problems for the Polonyi Potential, Phys. Lett. B 131 (1983) 59 [INSPIRE].
A.S. Goncharov, A.D. Linde and M.I. Vysotsky, Cosmological Problems For Spontaneously Broken Supergravity, Phys. Lett. B 147 (1984) 279 [INSPIRE].
J.R. Ellis, D.V. Nanopoulos and M. Quiros, On the Axion, Dilaton, Polonyi, Gravitino and Shadow Matter Problems in Supergravity and Superstring Models, Phys. Lett. B 174 (1986) 176 [INSPIRE].
T. Banks, D.B. Kaplan and A.E. Nelson, Cosmological implications of dynamical supersymmetry breaking, Phys. Rev. D 49 (1994) 779 [hep-ph/9308292] [INSPIRE].
B. de Carlos, J.A. Casas, F. Quevedo and E. Roulet, Model independent properties and cosmological implications of the dilaton and moduli sectors of 4-d strings, Phys. Lett. B 318 (1993) 447 [hep-ph/9308325] [INSPIRE].
H. Otsuka and Y. Sakamura, Spacetime evolution during moduli stabilization in radiation dominated era beyond 4D effective theory, JHEP 08 (2022) 120 [arXiv:2205.00175] [INSPIRE].
V. Kumar, D.R. Morrison and W. Taylor, Global aspects of the space of 6D \( \mathcal{N} \) = 1 supergravities, JHEP 2010 (2010) 118 [arXiv:1008.1062].
Y. Aghababaie, C.P. Burgess, S.L. Parameswaran and F. Quevedo, Towards a naturally small cosmological constant from branes in 6-D supergravity, Nucl. Phys. B 680 (2004) 389 [hep-th/0304256] [INSPIRE].
C.P. Burgess, Supersymmetric large extra dimensions and the cosmological constant: An Update, Annals Phys. 313 (2004) 283 [hep-th/0402200] [INSPIRE].
J. Garriga and M. Porrati, Football shaped extra dimensions and the absence of self-tuning, JHEP 08 (2004) 028 [hep-th/0406158] [INSPIRE].
C.P. Burgess, F. Quevedo, G. Tasinato and I. Zavala, General axisymmetric solutions and self-tuning in 6D chiral gauged supergravity, JHEP 11 (2004) 069 [hep-th/0408109] [INSPIRE].
G.W. Gibbons, R. Gueven and C.N. Pope, 3-branes and uniqueness of the Salam-Sezgin vacuum, Phys. Lett. B 595 (2004) 498 [hep-th/0307238] [INSPIRE].
Y. Aghababaie et al., Warped brane worlds in six-dimensional supergravity, JHEP 09 (2003) 037 [hep-th/0308064] [INSPIRE].
H.M. Lee and C. Ludeling, The General warped solution with conical branes in six-dimensional supergravity, JHEP 01 (2006) 062 [hep-th/0510026] [INSPIRE].
Acknowledgments
H. O. was supported in part by JSPS KAKENHI Grant Numbers JP20K14477 and the Education and Research Program for Mathematical and Data Science from the Kyushu University.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.14314
Rights and permissions
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.
About this article
Cite this article
Otsuka, H., Sakamura, Y. Full higher-dimensional analysis of moduli oscillation and radiation in expanding universe. J. High Energ. Phys. 2023, 231 (2023). https://doi.org/10.1007/JHEP05(2023)231
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)231