Abstract
In this note, we discuss the implications of the weak gravity conjecture (WGC) for general models of large-field inflation with a large number of axions N. We first show that, from the bottom-up perspective, such models admit a variety of different regimes for the enhancement of the effective axion decay constant, depending on the amount of alignment and the number of instanton terms that contribute to the scalar potential. This includes regimes of no enhancement, power-law enhancement and exponential enhancement with respect to N. As special cases, we recover the Pythagorean enhancement of N-flation, the N and N 3/2 enhancements derived by Bachlechner, Long and McAllister and the exponential enhancement by Choi, Kim and Yun. We then analyze which top-down constraints are put on such models from the requirement of consistency with quantum gravity. In particular, the WGC appears to imply that the enhancement of the effective axion decay constant must not grow parametrically with N for N ≫ 1. On the other hand, recent works proposed that axions might be able to violate this bound under certain circumstances. Our general expression for the enhancement allows us to translate this possibility into a condition on the number of instantons that couple to the axions. We argue that, at large N , models consistent with quantum gravity must either allow super-Planckian field excursions or have an enormous, possibly even exponentially large, number of dominant instanton terms in the scalar potential.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
BICEP2, Planck collaborations, P. Ade et al., Joint Analysis of BICEP2/Keck Array and Planck Data, Phys. Rev. Lett. 114 (2015) 101301 [arXiv:1502.00612] [INSPIRE].
D.H. Lyth, What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?, Phys. Rev. Lett. 78 (1997) 1861 [hep-ph/9606387] [INSPIRE].
D. Baumann and L. McAllister, Inflation and String Theory, arXiv:1404.2601.
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [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].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
J.P. Conlon, Quantum Gravity Constraints on Inflation, JCAP 09 (2012) 019 [arXiv:1203.5476] [INSPIRE].
C. Cheung and G.N. Remmen, Naturalness and the Weak Gravity Conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
T. Rudelius, On the Possibility of Large Axion Moduli Spaces, JCAP 04 (2015) 049 [arXiv:1409.5793] [INSPIRE].
A. de la Fuente, P. Saraswat and R. Sundrum, Natural Inflation and Quantum Gravity, Phys. Rev. Lett. 114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].
T. Rudelius, Constraints on Axion Inflation from the Weak Gravity Conjecture, JCAP 09 (2015) 020 [arXiv:1503.00795] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP 08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation, JHEP 10 (2015) 023 [arXiv:1503.04783] [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian Axions and the Weak Gravity Conjecture, JHEP 01 (2016) 091 [arXiv:1503.07853] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Winding out of the Swamp: Evading the Weak Gravity Conjecture with F-term Winding Inflation?, Phys. Lett. B 748 (2015) 455 [arXiv:1503.07912] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture, arXiv:1504.00659 [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian Axions in String Theory, JHEP 12 (2015) 042 [arXiv:1412.1093] [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].
L. McAllister, E. Silverstein and A. Westphal, Gravity Waves and Linear Inflation from Axion Monodromy, Phys. Rev. D 82 (2010) 046003 [arXiv:0808.0706] [INSPIRE].
F. Marchesano, G. Shiu and A.M. Uranga, F-term Axion Monodromy Inflation, JHEP 09 (2014) 184 [arXiv:1404.3040] [INSPIRE].
R. Blumenhagen and E. Plauschinn, Towards Universal Axion Inflation and Reheating in String Theory, Phys. Lett. B 736 (2014) 482 [arXiv:1404.3542] [INSPIRE].
A. Hebecker, S.C. Kraus and L.T. Witkowski, D7-Brane Chaotic Inflation, Phys. Lett. B 737 (2014) 16 [arXiv:1404.3711] [INSPIRE].
J.E. Kim, H.P. Nilles and M. Peloso, Completing natural inflation, JCAP 01 (2005) 005 [hep-ph/0409138] [INSPIRE].
G. Shiu, W. Staessens and F. Ye, Widening the Axion Window via Kinetic and Stückelberg Mixings, Phys. Rev. Lett. 115 (2015) 181601 [arXiv:1503.01015] [INSPIRE].
G. Shiu, W. Staessens and F. Ye, Large Field Inflation from Axion Mixing, JHEP 06 (2015) 026 [arXiv:1503.02965] [INSPIRE].
S. Dimopoulos, S. Kachru, J. McGreevy and J.G. Wacker, N-flation, JCAP 08 (2008) 003 [hep-th/0507205] [INSPIRE].
T.W. Grimm, Axion inflation in type-II string theory, Phys. Rev. D 77 (2008) 126007 [arXiv:0710.3883] [INSPIRE].
K. Choi, H. Kim and S. Yun, Natural inflation with multiple sub-Planckian axions, Phys. Rev. D 90 (2014) 023545 [arXiv:1404.6209] [INSPIRE].
T. Higaki and F. Takahashi, Natural and Multi-Natural Inflation in Axion Landscape, JHEP 07 (2014) 074 [arXiv:1404.6923] [INSPIRE].
T.W. Grimm, Axion Inflation in F-theory, Phys. Lett. B 739 (2014) 201 [arXiv:1404.4268] [INSPIRE].
S.H.H. Tye and S.S.C. Wong, Helical Inflation and Cosmic Strings, arXiv:1404.6988 [INSPIRE].
R. Kappl, S. Krippendorf and H.P. Nilles, Aligned Natural Inflation: Monodromies of two Axions, Phys. Lett. B 737 (2014) 124 [arXiv:1404.7127] [INSPIRE].
I. Ben-Dayan, F.G. Pedro and A. Westphal, Hierarchical Axion Inflation, Phys. Rev. Lett. 113 (2014) 261301 [arXiv:1404.7773] [INSPIRE].
M. Cicoli, K. Dutta and A. Maharana, N-flation with Hierarchically Light Axions in String Compactifications, JCAP 08 (2014) 012 [arXiv:1401.2579] [INSPIRE].
T.C. Bachlechner, M. Dias, J. Frazer and L. McAllister, Chaotic inflation with kinetic alignment of axion fields, Phys. Rev. D 91 (2015) 023520 [arXiv:1404.7496] [INSPIRE].
X. Gao, T. Li and P. Shukla, Combining Universal and Odd RR Axions for Aligned Natural Inflation, JCAP 10 (2014) 048 [arXiv:1406.0341] [INSPIRE].
M. Peloso and C. Unal, Trajectories with suppressed tensor-to-scalar ratio in Aligned Natural Inflation, JCAP 06 (2015) 040 [arXiv:1504.02784] [INSPIRE].
N. Kaloper, A. Lawrence and L. Sorbo, An Ignoble Approach to Large Field Inflation, JCAP 03 (2011) 023 [arXiv:1101.0026] [INSPIRE].
R. Blumenhagen, D. Herschmann and E. Plauschinn, The Challenge of Realizing F-term Axion Monodromy Inflation in String Theory, JHEP 01 (2015) 007 [arXiv:1409.7075] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Tuning and Backreaction in F-term Axion Monodromy Inflation, Nucl. Phys. B 894 (2015) 456 [arXiv:1411.2032] [INSPIRE].
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
G. Dvali, Black Holes and Large-N Species Solution to the Hierarchy Problem, Fortsch. Phys. 58 (2010) 528 [arXiv:0706.2050] [INSPIRE].
X. Dong, B. Horn, E. Silverstein and A. Westphal, Simple exercises to flatten your potential, Phys. Rev. D 84 (2011) 026011 [arXiv:1011.4521] [INSPIRE].
W. Buchmüller, E. Dudas, L. Heurtier, A. Westphal, C. Wieck and M.W. Winkler, Challenges for Large-Field Inflation and Moduli Stabilization, JHEP 04 (2015) 058 [arXiv:1501.05812] [INSPIRE].
T. Cai, J. Fan, T. Jiang and T. Zhang, Distributions of Angles in Random Packing on Spheres, arXiv:1306.0256.
J.E. Goodman and J. O’Rourke, Handbook of Discrete and Computational Geometry, Chapman & Hall/CRC (2004).
E. Miller, V. Reiner and B. Sturmfels, Geometric Combinatorics, American Mathematical Society (2007).
J. Morton, L. Pachter, A. Shiu and B. Sturmfels, The Cyclohedron Test for Finding Periodic Genes in Time Course Expression Studies, q-bio/0702049.
D.W. Barnette, The minimum number of vertices of a simple polytope, Israel J. Math. 10 (1971) 121.
D.W. Barnette, A proof of the lower bound conjecture for convex polytopes, Pac. J. Math. 46 (1973) 349.
F. Denef, M.R. Douglas, B. Florea, A. Grassi and S. Kachru, Fixing all moduli in a simple F-theory compactification, Adv. Theor. Math. Phys. 9 (2005) 861 [hep-th/0503124] [INSPIRE].
M. Bianchi, A. Collinucci and L. Martucci, Magnetized E3-brane instantons in F-theory, JHEP 12 (2011) 045 [arXiv:1107.3732] [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: 1504.03566
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
Junghans, D. Large-field inflation with multiple axions and the weak gravity conjecture. J. High Energ. Phys. 2016, 128 (2016). https://doi.org/10.1007/JHEP02(2016)128
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)128