Abstract
Observable B-mode polarization in the CMBR would point to a high scale of inflation and large field excursions during the inflationary era. Non-compact string moduli spaces are a suggestive setting for these phenomena. Although they are unlikely to be described by weak coupling models, effective field theories compatible with known features of cosmology do exist. These models can be viewed as generalizations to a large field regime of hybrid inflation. We note close parallels to small and large field axion models. This paper outlines the requirements for successful modular inflation, and gives examples of effective field theories which satisfy them. The required tunings are readily characterized. These models can also be thought of as models of chaotic inflation, in a way we describe. In the modular framework, one would expect that any would-be Peccei-Quinn symmetry would likely be badly broken during inflation, and the axion would have Hubble scale mass; in this situation, isocurvature fluctuations would be suppressed and the initial misalignment angle would be fixed, rather than being a random variable.
Article PDF
Similar content being viewed by others
References
D.H. Lyth, Particle physics models of inflation, Lect. Notes Phys. 738 (2008) 81 [hep-th/0702128] [INSPIRE].
BICEP2 collaboration, P.A.R. Ade et al., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].
BICEP2 and Planck collaborations, P.A.R. Ade et al., Joint analysis of BICEP2/Keck Array and Planck data, Phys. Rev. Lett. 114 (2015) 101301 [arXiv:1502.00612] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, Astron. Astrophys. 571 (2014) A22 [arXiv:1303.5082] [INSPIRE].
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].
A.D. Linde, Chaotic inflation, Phys. Lett. B 129 (1983) 177 [INSPIRE].
T. Banks, M. Dine, P.J. Fox and E. Gorbatov, On the possibility of large axion decay constants, JCAP 06 (2003) 001 [hep-th/0303252] [INSPIRE].
K.-Y. Choi and B. Kyae, Large tensor spectrum of BICEP2 in the natural SUSY hybrid model, Phys. Rev. D 90 (2014) 023536 [arXiv:1404.7855] [INSPIRE].
E. Silverstein and A. Westphal, Monodromy in the CMB: gravity waves and string inflation, Phys. Rev. D 78 (2008) 106003 [arXiv:0803.3085] [INSPIRE].
J.E. Kim, H.P. Nilles and M. Peloso, Completing natural inflation, JCAP 01 (2005) 005 [hep-ph/0409138] [INSPIRE].
A. Ashoorioon and M.M. Sheikh-Jabbari, Gauged M-flation after BICEP2, Phys. Lett. B 739 (2014) 391 [arXiv:1405.1685] [INSPIRE].
A. Ashoorioon, K. Dimopoulos, M.M. Sheikh-Jabbari and G. Shiu, Reconciliation of high energy scale models of inflation with Planck, JCAP 02 (2014) 025 [arXiv:1306.4914] [INSPIRE].
S. Clesse and J. Rekier, Updated constraints on large field hybrid inflation, Phys. Rev. D 90 (2014) 083527 [arXiv:1407.1984] [INSPIRE].
A. Saltman and E. Silverstein, A new handle on de Sitter compactifications, JHEP 01 (2006) 139 [hep-th/0411271] [INSPIRE].
M. Dine, L. Randall and S.D. Thomas, Supersymmetry breaking in the early universe, Phys. Rev. Lett. 75 (1995) 398 [hep-ph/9503303] [INSPIRE].
T. Banks, Remarks on M theoretic cosmology, hep-th/9906126 [INSPIRE].
M. Cicoli and F. Quevedo, String moduli inflation: an overview, Class. Quant. Grav. 28 (2011) 204001 [arXiv:1108.2659] [INSPIRE].
C.P. Burgess, M. Cicoli, F. Quevedo and M. Williams, Inflating with large effective fields, JCAP 11 (2014) 045 [arXiv:1404.6236] [INSPIRE].
M. Dine and L. Pack, Studies in small field inflation, JCAP 06 (2012) 033 [arXiv:1109.2079] [INSPIRE].
M. Dine and N. Seiberg, Is the superstring weakly coupled?, Phys. Lett. B 162 (1985) 299 [INSPIRE].
P. Fox, A. Pierce and S.D. Thomas, Probing a QCD string axion with precision cosmological measurements, hep-th/0409059 [INSPIRE].
M. Dine and A. Anisimov, Is there a Peccei-Quinn phase transition?, JCAP 07 (2005) 009 [hep-ph/0405256] [INSPIRE].
L.M. Carpenter and S. Raby, Chaotic hybrid inflation with a gauged B-L, Phys. Lett. B 738 (2014) 109 [arXiv:1405.6143] [INSPIRE].
M.P. Hertzberg and F. Wilczek, Inflation driven by unification energy, arXiv:1407.6010 [INSPIRE].
A.D. Linde, Hybrid inflation, Phys. Rev. D 49 (1994) 748 [astro-ph/9307002] [INSPIRE].
E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart and D. Wands, False vacuum inflation with Einstein gravity, Phys. Rev. D 49 (1994) 6410 [astro-ph/9401011] [INSPIRE].
G.R. Dvali, Q. Shafi and R.K. Schaefer, Large scale structure and supersymmetric inflation without fine tuning, Phys. Rev. Lett. 73 (1994) 1886 [hep-ph/9406319] [INSPIRE].
D.H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rept. 314 (1999) 1 [hep-ph/9807278] [INSPIRE].
K. Kumekawa, T. Moroi and T. Yanagida, Flat potential for inflaton with a discrete R invariance in supergravity, Prog. Theor. Phys. 92 (1994) 437 [hep-ph/9405337] [INSPIRE].
M. Bose, M. Dine, A. Monteux and L.S. Haskins, Small field inflation and the spectral index, JCAP 01 (2014) 038 [arXiv:1310.2609] [INSPIRE].
C. Pallis and Q. Shafi, Update on minimal supersymmetric hybrid inflation in light of Planck, Phys. Lett. B 725 (2013) 327 [arXiv:1304.5202] [INSPIRE].
L. Boubekeur and D. Lyth, Hilltop inflation, JCAP 07 (2005) 010 [hep-ph/0502047] [INSPIRE].
A.D. Linde and A. Riotto, Hybrid inflation in supergravity, Phys. Rev. D 56 (1997) 1841 [hep-ph/9703209] [INSPIRE].
L.M. Carpenter, M. Dine, G. Festuccia and L. Ubaldi, Axions in gauge mediation, Phys. Rev. D 80 (2009) 125023 [arXiv:0906.5015] [INSPIRE].
G. Lazarides, C. Panagiotakopoulos and Q. Shafi, Phenomenology and cosmology with superstrings, Phys. Rev. Lett. 56 (1986) 432 [INSPIRE].
M. Dine, Problems of naturalness: some lessons from string theory, hep-th/9207045 [INSPIRE].
E. Witten, Some properties of O(32) superstrings, Phys. Lett. B 149 (1984) 351 [INSPIRE].
K. Bobkov, V. Braun, P. Kumar and S. Raby, Stabilizing all Kähler moduli in type IIB orientifolds, JHEP 12 (2010) 056 [arXiv:1003.1982] [INSPIRE].
M. Dine, G. Festuccia, J. Kehayias and W. Wu, Axions in the landscape and string theory, JHEP 01 (2011) 012 [arXiv:1010.4803] [INSPIRE].
N.V. Krasnikov, On supersymmetry breaking in superstring theories, Phys. Lett. B 193 (1987) 37 [INSPIRE].
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].
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].
R. Brustein and P.J. Steinhardt, Challenges for superstring cosmology, Phys. Lett. B 302 (1993) 196 [hep-th/9212049] [INSPIRE].
T. Banks and M. Dine, Dark energy in perturbative string cosmology, JHEP 10 (2001) 012 [hep-th/0106276] [INSPIRE].
T. Banks, Landskepticism or why effective potentials don’t count string models, hep-th/0412129 [INSPIRE].
T. Banks and M. Dine, Coping with strongly coupled string theory, Phys. Rev. D 50 (1994) 7454 [hep-th/9406132] [INSPIRE].
T. Banks and W. Fischler, The holographic approach to cosmology, hep-th/0412097 [INSPIRE].
K. Bamba, S. Nojiri and S.D. Odintsov, Reconstruction of scalar field theories realizing inflation consistent with the Planck and BICEP2 results, Phys. Lett. B 737 (2014) 374 [arXiv:1406.2417] [INSPIRE].
A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [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: 1408.0046
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
Dine, M., Stephenson-Haskins, L. Hybrid inflation with Planck scale fields. J. High Energ. Phys. 2015, 208 (2015). https://doi.org/10.1007/JHEP09(2015)208
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2015)208