Abstract
We study inflationary models where the kinetic sector of the theory has a non-linearly realised symmetry which is broken by the inflationary potential. We distinguish between kinetic symmetries which non-linearly realise an internal or space-time group, and which yield a flat or curved scalar manifold. This classification leads to well-known inflationary models such as monomial inflation and α-attractors, as well as a new model based on fixed couplings between a dilaton and many axions which non-linearly realises higher-dimensional conformal symmetries. In this model, inflation can be realised along the dilatonic direction, leading to a tensor-to-scalar ratio r ∼ 0.01 and a spectral index n s ∼ 0.975. We refer to the new model as ambient inflation since inflation proceeds along an isometry of an anti-de Sitter ambient space-time, which fully determines the kinetic sector.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current, Phys. Rev. 137 (1965) B1022 [INSPIRE].
C. Cheung, K. Kampf, J. Novotny and J. Trnka, Effective Field Theories from Soft Limits of Scattering Amplitudes, Phys. Rev. Lett. 114 (2015) 221602 [arXiv:1412.4095] [INSPIRE].
K. Hinterbichler and A. Joyce, Hidden symmetry of the Galileon, Phys. Rev. D 92 (2015) 023503 [arXiv:1501.07600] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A Periodic Table of Effective Field Theories, JHEP 02 (2017) 020 [arXiv:1611.03137] [INSPIRE].
A. Padilla, D. Stefanyszyn and T. Wilson, Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes, JHEP 04 (2017) 015 [arXiv:1612.04283] [INSPIRE].
A.D. Linde, Chaotic Inflation, Phys. Lett. B 129 (1983) 177 [INSPIRE].
A.D. Linde, Chaotic Inflation With Constrained Fields, Phys. Lett. B 202 (1988) 194 [INSPIRE].
N. Kaloper, A. Lawrence and L. Sorbo, An Ignoble Approach to Large Field Inflation, JCAP 03 (2011) 023 [arXiv:1101.0026] [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].
BICEP2, Keck Array collaborations, P.A.R. Ade et al., Improved Constraints on Cosmology and Foregrounds from BICEP2 and Keck Array Cosmic Microwave Background Data with Inclusion of 95 GHz Band, Phys. Rev. Lett. 116 (2016) 031302 [arXiv:1510.09217] [INSPIRE].
C.P. Burgess, M. Cicoli, F. Quevedo and M. Williams, Inflating with Large Effective Fields, JCAP 11 (2014) 045 [arXiv:1404.6236] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
J. Sonner and P.K. Townsend, Dilaton domain walls and dynamical systems, Class. Quant. Grav. 23 (2006) 441 [hep-th/0510115] [INSPIRE].
S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177 (1969) 2239 [INSPIRE].
C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev. 177 (1969) 2247 [INSPIRE].
D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3 [INSPIRE].
E.A. Ivanov and V.I. Ogievetsky, The Inverse Higgs Phenomenon in Nonlinear Realizations, Teor. Mat. Fiz. 25 (1975) 164 [INSPIRE].
C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan and L. Senatore, The Effective Field Theory of Inflation, JHEP 03 (2008) 014 [arXiv:0709.0293] [INSPIRE].
L. Senatore and M. Zaldarriaga, The Effective Field Theory of Multifield Inflation, JHEP 04 (2012) 024 [arXiv:1009.2093] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, Superconformal Inflationary α-Attractors, JHEP 11 (2013) 198 [arXiv:1311.0472] [INSPIRE].
R. Kallosh and A. Linde, Cosmological Attractors and Asymptotic Freedom of the Inflaton Field, JCAP 06 (2016) 047 [arXiv:1604.00444] [INSPIRE].
R. Kallosh, A.D. Linde, D.A. Linde and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52 (1995) 912 [hep-th/9502069] [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].
N. Kaloper and L. Sorbo, A Natural Framework for Chaotic Inflation, Phys. Rev. Lett. 102 (2009) 121301 [arXiv:0811.1989] [INSPIRE].
M. Berg, E. Pajer and S. Sjors, Dante’s Inferno, Phys. Rev. D 81 (2010) 103535 [arXiv:0912.1341] [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].
N. Kaloper and A. Lawrence, London equation for monodromy inflation, Phys. Rev. D 95 (2017) 063526 [arXiv:1607.06105] [INSPIRE].
G. D’Amico, N. Kaloper and A. Lawrence, Monodromy inflation at strong coupling: 4π in the sky, arXiv:1709.07014 [INSPIRE].
R. Klein, D. Roest and D. Stefanyszyn, Spontaneously Broken Spacetime Symmetries and the Role of Inessential Goldstones, JHEP 10 (2017) 051 [arXiv:1709.03525] [INSPIRE].
G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Galileons as Wess-Zumino Terms, JHEP 06 (2012) 004 [arXiv:1203.3191] [INSPIRE].
K. Hinterbichler, M. Trodden and D. Wesley, Multi-field galileons and higher co-dimension branes, Phys. Rev. D 82 (2010) 124018 [arXiv:1008.1305] [INSPIRE].
C. de Rham and A.J. Tolley, DBI and the Galileon reunited, JCAP 05 (2010) 015 [arXiv:1003.5917] [INSPIRE].
S. Bellucci, E. Ivanov and S. Krivonos, AdS/CFT equivalence transformation, Phys. Rev. D 66 (2002) 086001 [Erratum ibid. D 67 (2003) 049901] [hep-th/0206126] [INSPIRE].
P. Creminelli, M. Serone and E. Trincherini, Non-linear Representations of the Conformal Group and Mapping of Galileons, JHEP 10 (2013) 040 [arXiv:1306.2946] [INSPIRE].
M. Alishahiha, E. Silverstein and D. Tong, DBI in the sky, Phys. Rev. D 70 (2004) 123505 [hep-th/0404084] [INSPIRE].
C. Csáki, N. Kaloper, J. Serra and J. Terning, Inflation from Broken Scale Invariance, Phys. Rev. Lett. 113 (2014) 161302 [arXiv:1406.5192] [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].
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].
J. García-Bellido and D. Roest, Large-N running of the spectral index of inflation, Phys. Rev. D 89 (2014) 103527 [arXiv:1402.2059] [INSPIRE].
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].
D. Roest, Universality classes of inflation, JCAP 01 (2014) 007 [arXiv:1309.1285] [INSPIRE].
M. Galante, R. Kallosh, A. Linde and D. Roest, Unity of Cosmological Inflation Attractors, Phys. Rev. Lett. 114 (2015) 141302 [arXiv:1412.3797] [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].
T. Terada, Generalized Pole Inflation: Hilltop, Natural and Chaotic Inflationary Attractors, Phys. Lett. B 760 (2016) 674 [arXiv:1602.07867] [INSPIRE].
S. Ferrara, R. Kallosh, A. Linde and M. Porrati, Minimal Supergravity Models of Inflation, Phys. Rev. D 88 (2013) 085038 [arXiv:1307.7696] [INSPIRE].
S. Ferrara and R. Kallosh, Seven-disk manifold, α-attractors and B modes, Phys. Rev. D 94 (2016) 126015 [arXiv:1610.04163] [INSPIRE].
R. Kallosh, A. Linde, T. Wrase and Y. Yamada, Maximal Supersymmetry and B-Mode Targets, JHEP 04 (2017) 144 [arXiv:1704.04829] [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. 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].
D. Klaewer and E. Palti, Super-Planckian Spatial Field Variations and Quantum Gravity, JHEP 01 (2017) 088 [arXiv:1610.00010] [INSPIRE].
A. Achúcarro, R. Kallosh, A. Linde, D.-G. Wang and Y. Welling, Universality of multi-field α-attractors, JCAP 04 (2018) 028 [arXiv:1711.09478] [INSPIRE].
J. Ellis, D.V. Nanopoulos and K.A. Olive, No-Scale Supergravity Realization of the Starobinsky Model of Inflation, Phys. Rev. Lett. 111 (2013) 111301 [Erratum ibid. 111 (2016) 129902] [arXiv:1305.1247] [INSPIRE].
J. Ellis, D.V. Nanopoulos and K.A. Olive, Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity, JCAP 10 (2013) 009 [arXiv:1307.3537] [INSPIRE].
E. McDonough and M. Scalisi, Inflation from Nilpotent Kähler Corrections, JCAP 11 (2016) 028 [arXiv:1609.00364] [INSPIRE].
R. Kallosh, A. Linde, D. Roest and Y. Yamada, D3 induced geometric inflation, JHEP 07 (2017) 057 [arXiv:1705.09247] [INSPIRE].
C.P. Burgess, M. Cicoli, S. de Alwis and F. Quevedo, Robust Inflation from Fibrous Strings, JCAP 05 (2016) 032 [arXiv:1603.06789] [INSPIRE].
R. Kallosh, A. Linde, D. Roest, A. Westphal and Y. Yamada, Fibre Inflation and α-attractors, JHEP 02 (2018) 117 [arXiv:1707.05830] [INSPIRE].
M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
R. Bravo, S. Mooij, G.A. Palma and B. Pradenas, A generalized non-Gaussian consistency relation for single field inflation, JCAP 05 (2018) 024 [arXiv:1711.02680] [INSPIRE].
B. Finelli, G. Goon, E. Pajer and L. Santoni, Soft Theorems For Shift-Symmetric Cosmologies, Phys. Rev. D 97 (2018) 063531 [arXiv:1711.03737] [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: 1712.05760
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
Klein, R., Roest, D. & Stefanyszyn, D. Symmetry breaking patterns for inflation. J. High Energ. Phys. 2018, 6 (2018). https://doi.org/10.1007/JHEP06(2018)006
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)006