Abstract
In negatively curved field spaces, inflation can be realised even in steep potentials. Hyperinflation invokes the ‘centrifugal force’ of a field orbiting the hyperbolic plane to sustain inflation. We generalise hyperinflation by showing that it can be realised in models with any number of fields (Nf ≥ 2), and in broad classes of potentials that, in particular, don’t need to be rotationally symmetric. For example, hyperinflation can follow a period of radial slow-roll inflation that undergoes geometric destabilisation, yet this inflationary phase is not identical to the recently proposed scenario of ‘side-tracked inflation’. We furthermore provide a detailed proof of the attractor mechanism of (the original and generalised) hyperinflation, and provide a novel set of characteristic, explicit models. We close by discussing the compatibility of hyperinflation with observations and the recently much discussed ‘swampland conjectures’. Observationally viable models can be realised that satisfy either the ‘de Sitter conjecture’ (V′/V ≳ 1) or the ‘distance conjecture’ (Δϕ ≲ 1), but satisfying both simultaneously brings hyperinflation in some tension with successful reheating after inflation. However, hyperinflation can get much closer to satisfying all of these criteria than standard slow-roll inflation. Furthermore, while the original model is in stark tension with the weak gravity conjecture, generalisations can circumvent this issue.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Kallosh and A.D. Linde, Universality Class in Conformal Inflation, JCAP 07 (2013) 002 [arXiv:1306.5220] [INSPIRE].
R. Kallosh and A.D. Linde, Multi-field Conformal Cosmological Attractors, JCAP 12 (2013) 006 [arXiv:1309.2015] [INSPIRE].
R. Kallosh, A.D. Linde and D. Roest, Superconformal Inflationary α-Attractors, JHEP 11 (2013) 198 [arXiv:1311.0472] [INSPIRE].
R. Kallosh, A.D. Linde and D. Roest, Large field inflation and double α-attractors, JHEP 08 (2014) 052 [arXiv:1405.3646] [INSPIRE].
M. Galante, R. Kallosh, A.D. Linde and D. Roest, Unity of Cosmological Inflation Attractors, Phys. Rev. Lett. 114 (2015) 141302 [arXiv:1412.3797] [INSPIRE].
J.J.M. Carrasco, R. Kallosh, A.D. Linde and D. Roest, Hyperbolic geometry of cosmological attractors, Phys. Rev. D 92 (2015) 041301 [arXiv:1504.05557] [INSPIRE].
S. Renaux-Petel and K. Turzynski, Geometrical Destabilization of Inflation, Phys. Rev. Lett. 117 (2016) 141301 [arXiv:1510.01281] [INSPIRE].
A.D. Linde, Single-field α-attractors, JCAP 05 (2015) 003 [arXiv:1504.00663] [INSPIRE].
J.J.M. Carrasco, R. Kallosh and A.D. Linde, Cosmological Attractors and Initial Conditions for Inflation, Phys. Rev. D 92 (2015) 063519 [arXiv:1506.00936] [INSPIRE].
B.J. Broy, M. Galante, D. Roest and A. Westphal, Pole inflation — Shift symmetry and universal corrections, JHEP 12 (2015) 149 [arXiv:1507.02277] [INSPIRE].
D. Roest and M. Scalisi, Cosmological attractors from α-scale supergravity, Phys. Rev. D 92 (2015) 043525 [arXiv:1503.07909] [INSPIRE].
M. Dias, J. Frazer and D. Seery, Computing observables in curved multifield models of inflation — A guide (with code) to the transport method, JCAP 12 (2015) 030 [arXiv:1502.03125] [INSPIRE].
R. Kallosh, A.D. Linde, D. Roest and T. Wrase, Sneutrino inflation with α-attractors, JCAP 11 (2016) 046 [arXiv:1607.08854] [INSPIRE].
A.D. Linde, Random Potentials and Cosmological Attractors, JCAP 02 (2017) 028 [arXiv:1612.04505] [INSPIRE].
R. Kallosh and A.D. Linde, Cosmological Attractors and Asymptotic Freedom of the Inflaton Field, JCAP 06 (2016) 047 [arXiv:1604.00444] [INSPIRE].
A.R. Brown, Hyperbolic Inflation, Phys. Rev. Lett. 121 (2018) 251601 [arXiv:1705.03023] [INSPIRE].
S. Mizuno and S. Mukohyama, Primordial perturbations from inflation with a hyperbolic field-space, Phys. Rev. D 96 (2017) 103533 [arXiv:1707.05125] [INSPIRE].
R. Kallosh, A.D. Linde, D. Roest, A. Westphal and Y. Yamada, Fibre Inflation and α-attractors, JHEP 02 (2018) 117 [arXiv:1707.05830] [INSPIRE].
A. Achúcarro, R. Kallosh, A.D. Linde, D.-G. Wang and Y. Welling, Universality of multi-field α -attractors, JCAP 04 (2018) 028 [arXiv:1711.09478] [INSPIRE].
S. Renaux-Petel, K. Turzynski and V. Vennin, Geometrical destabilization, premature end of inflation and Bayesian model selection, JCAP 11 (2017) 006 [arXiv:1706.01835] [INSPIRE].
A.D. Linde, D.-G. Wang, Y. Welling, Y. Yamada and A. Achúcarro, Hypernatural inflation, JCAP 07 (2018) 035 [arXiv:1803.09911] [INSPIRE].
A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, JCAP 02 (2019) 041 [arXiv:1807.04390] [INSPIRE].
P. Christodoulidis, D. Roest and E.I. Sfakianakis, Angular inflation in multi-field α-attractors, arXiv:1803.09841 [INSPIRE].
S. Garcia-Saenz, S. Renaux-Petel and J. Ronayne, Primordial fluctuations and non-Gaussianities in sidetracked inflation, JCAP 07 (2018) 057 [arXiv:1804.11279] [INSPIRE].
S. Garcia-Saenz and S. Renaux-Petel, Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of sound, JCAP 11 (2018) 005 [arXiv:1805.12563] [INSPIRE].
M. Dias, J. Frazer, A. Retolaza, M. Scalisi and A. Westphal, Pole N-flation, JHEP 02 (2019) 120 [arXiv:1805.02659] [INSPIRE].
X. Chen, G.A. Palma, W. Riquelme, B. Scheihing Hitschfeld and S. Sypsas, Landscape tomography through primordial non-Gaussianity, Phys. Rev. D 98 (2018) 083528 [arXiv:1804.07315] [INSPIRE].
X. Chen, G.A. Palma, B. Scheihing Hitschfeld and S. Sypsas, Reconstructing the Inflationary Landscape with Cosmological Data, Phys. Rev. Lett. 121 (2018) 161302 [arXiv:1806.05202] [INSPIRE].
S. Cremonini, Z. Lalak and K. Turzynski, Strongly Coupled Perturbations in Two-Field Inflationary Models, JCAP 03 (2011) 016 [arXiv:1010.3021] [INSPIRE].
D.I. Kaiser and E.I. Sfakianakis, Multifield Inflation after Planck: The Case for Nonminimal Couplings, Phys. Rev. Lett. 112 (2014) 011302 [arXiv:1304.0363] [INSPIRE].
D. Baumann and L. McAllister, Inflation and String Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2015) [arXiv:1404.2601] [INSPIRE].
A. Achúcarro, V. Atal, C. Germani and G.A. Palma, Cumulative effects in inflation with ultra-light entropy modes, JCAP 02 (2017) 013 [arXiv:1607.08609] [INSPIRE].
G.K. Karananas and J. Rubio, On the geometrical interpretation of scale-invariant models of inflation, Phys. Lett. B 761 (2016) 223 [arXiv:1606.08848] [INSPIRE].
D.A. Easson, R. Gregory, D.F. Mota, G. Tasinato and I. Zavala, Spinflation, JCAP 02 (2008) 010 [arXiv:0709.2666] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [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].
S. Groot Nibbelink and B.J.W. van Tent, Scalar perturbations during multiple field slow-roll inflation, Class. Quant. Grav. 19 (2002) 613 [hep-ph/0107272] [INSPIRE].
C. Gordon, D. Wands, B.A. Bassett and R. Maartens, Adiabatic and entropy perturbations from inflation, Phys. Rev. D 63 (2001) 023506 [astro-ph/0009131] [INSPIRE].
M. Sasaki and E.D. Stewart, A General analytic formula for the spectral index of the density perturbations produced during inflation, Prog. Theor. Phys. 95 (1996) 71 [astro-ph/9507001] [INSPIRE].
A.D. Linde, Hybrid inflation, Phys. Rev. D 49 (1994) 748 [astro-ph/9307002] [INSPIRE].
J. García-Bellido, A.D. Linde and D. Wands, Density perturbations and black hole formation in hybrid inflation, Phys. Rev. D 54 (1996) 6040 [astro-ph/9605094] [INSPIRE].
C.M. Peterson and M. Tegmark, Testing Two-Field Inflation, Phys. Rev. D 83 (2011) 023522 [arXiv:1005.4056] [INSPIRE].
C.M. Peterson and M. Tegmark, Testing multifield inflation: A geometric approach, Phys. Rev. D 87 (2013) 103507 [arXiv:1111.0927] [INSPIRE].
M.C.D. Marsh, L. McAllister, E. Pajer and T. Wrase, Charting an Inflationary Landscape with Random Matrix Theory, JCAP 11 (2013) 040 [arXiv:1307.3559] [INSPIRE].
M. Dias, J. Frazer and M.C.D. Marsh, Simple emergent power spectra from complex inflationary physics, Phys. Rev. Lett. 117 (2016) 141303 [arXiv:1604.05970] [INSPIRE].
M. Dias, J. Frazer and M.C.D. Marsh, Seven Lessons from Manyfield Inflation in Random Potentials, JCAP 01 (2018) 036 [arXiv:1706.03774] [INSPIRE].
T. Bjorkmo and M.C.D. Marsh, Manyfield Inflation in Random Potentials, JCAP 02 (2018) 037 [arXiv:1709.10076] [INSPIRE].
T. Bjorkmo and M.C.D. Marsh, Local, algebraic simplifications of Gaussian random fields, JCAP 12 (2018) 022 [arXiv:1805.03117] [INSPIRE].
A. Achúcarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Mass hierarchies and non-decoupling in multi-scalar field dynamics, Phys. Rev. D 84 (2011) 043502 [arXiv:1005.3848] [INSPIRE].
A. Achúcarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Features of heavy physics in the CMB power spectrum, JCAP 01 (2011) 030 [arXiv:1010.3693] [INSPIRE].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [INSPIRE].
Planck collaboration, Planck 2018 results. X. Constraints on inflation, arXiv:1807.06211 [INSPIRE].
P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the Cosmological Implications of the String Swampland, Phys. Lett. B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].
U.H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, arXiv:1807.05193 [INSPIRE].
F. Denef, A. Hebecker and T. Wrase, de Sitter swampland conjecture and the Higgs potential, Phys. Rev. D 98 (2018) 086004 [arXiv:1807.06581] [INSPIRE].
Y. Akrami, R. Kallosh, A.D. Linde and V. Vardanyan, The Landscape, the Swampland and the Era of Precision Cosmology, Fortsch. Phys. 67 (2019) 1800075 [arXiv:1808.09440] [INSPIRE].
M. Cicoli, S. De Alwis, A. Maharana, F. Muia and F. Quevedo, de Sitter vs. Quintessence in String Theory, Fortsch. Phys. 67 (2019) 1800079 [arXiv:1808.08967] [INSPIRE].
M.C.D. Marsh, The Swampland, Quintessence and the Vacuum Energy, Phys. Lett. B 789 (2019) 639 [arXiv:1809.00726] [INSPIRE].
P.F. de Salas, M. Lattanzi, G. Mangano, G. Miele, S. Pastor and O. Pisanti, Bounds on very low reheating scenarios after Planck, Phys. Rev. D 92 (2015) 123534 [arXiv:1511.00672] [INSPIRE].
T. Bjorkmo, The rapid-turn inflationary attractor, arXiv:1902.10529 [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: 1901.08603
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Bjorkmo, T., Marsh, M.C.D. Hyperinflation generalised: from its attractor mechanism to its tension with the ‘swampland conditions’. J. High Energ. Phys. 2019, 172 (2019). https://doi.org/10.1007/JHEP04(2019)172
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2019)172