Abstract
We determine the most general time-independent Noether symmetries of two-field cosmological models with rotationally-invariant scalar manifold metrics. In particular, we show that such models can have hidden symmetries, which arise if and only if the scalar manifold metric has Gaussian curvature −3/8, i.e. when the model is of elementary α-attractor type with a fixed value of the parameter α. In this case, we find explicitly all scalar potentials compatible with hidden Noether symmetries, thus classifying all models of this type. We also discuss some implications of the corresponding conserved quantity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on slow roll and the de Sitter swampland, arXiv:1807.05193 [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].
A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, JCAP02 (2019) 041 [arXiv:1807.04390] [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, Non-Gaussianity in two-field inflation, Phys. Rev.D 84 (2011) 023520 [arXiv:1011.6675] [INSPIRE].
A. Achucarro and Y. Welling, Multiple field inflation and signatures of heavy physics in the CMB, arXiv:1502.04369 [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].
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].
S. Cremonini, Z. Lalak and K. Turzynski, Strongly coupled perturbations in two-field inflationary models, JCAP03 (2011) 016 [arXiv:1010.3021] [INSPIRE].
Z. Lalak, D. Langlois, S. Pokorski and K. Turzynski, Curvature and isocurvature perturbations in two-field inflation, JCAP07 (2007) 014 [arXiv:0704.0212] [INSPIRE].
M. Dias, J. Frazer and D. Seery, Computing observables in curved multifield models of inflation — a guide (with code) to the transport method, JCAP12 (2015) 030 [arXiv:1502.03125] [INSPIRE].
M. Dias, J. Frazer, D.J. Mulryne and D. Seery, Numerical evaluation of the bispectrum in multiple field inflation — the transport approach with code, JCAP12 (2016) 033 [arXiv:1609.00379] [INSPIRE].
D.J. Mulryne and J.W. Ronayne, PyTransport: a python package for the calculation of inflationary correlation functions, arXiv:1609.00381 [INSPIRE].
K. Kainulainen, J. Leskinen, S. Nurmi and T. Takahashi, CMB spectral distortions in generic two-field models, JCAP11 (2017) 002 [arXiv:1707.01300] [INSPIRE].
E.M. Babalic and C.I. Lazaroiu, Cosmological flows on hyperbolic surfaces, arXiv:1810.00441 [INSPIRE].
P. Christodoulidis, D. Roest and E.I. Sfakianakis, Scaling attractors in multi-field inflation, arXiv:1903.06116 [INSPIRE].
P. Christodoulidis, D. Roest and E.I. Sfakianakis, Attractors, bifurcations and curvature in multi-field inflation, arXiv:1903.03513 [INSPIRE].
J. Palis Jr. and W. De Melo, Geometric theory of dynamical systems: an introduction, Springer, New York, U.S.A. (2012).
L. Anguelova, E.M. Babalic and C.I. Lazaroiu, Two-field cosmological α-attractors with Noether symmetry, JHEP04 (2019) 148 [arXiv:1809.10563] [INSPIRE].
C.I. Lazaroiu and C.S. Shahbazi, Generalized two-field α-attractor models from geometrically finite hyperbolic surfaces, Nucl. Phys.B 936 (2018) 542 [arXiv:1702.06484] [INSPIRE].
E.M. Babalic and C.I. Lazaroiu, Generalized α-attractor models from elementary hyperbolic surfaces, Adv. Math. Phys.2018 (2018) 7323090 [arXiv:1703.01650] [INSPIRE].
E.M. Babalic and C.I. Lazaroiu, Generalized two-field α-attractor models from the hyperbolic triply-punctured sphere, Nucl. Phys.B 937 (2018) 434 [arXiv:1703.06033] [INSPIRE].
E.M. Babalic and C.I. Lazaroiu, Two-field cosmological models and the uniformization theorem, Springer Proc. Math. Stat.255 (2017) 233 [arXiv:1801.03356] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, Superconformal inflationary α-attractors, JHEP11 (2013) 198 [arXiv:1311.0472] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, Large field inflation and double α-attractors, JHEP08 (2014) 052 [arXiv:1405.3646] [INSPIRE].
R. Kallosh and A. Linde, Universality class in conformal inflation, JCAP07 (2013) 002 [arXiv:1306.5220] [INSPIRE].
R. Kallosh and A. Linde, Multi-field conformal cosmological attractors, JCAP12 (2013) 006 [arXiv:1309.2015] [INSPIRE].
R. Kallosh and A. Linde, Escher in the sky, Comptes Rendus Physique16 (2015) 914 [arXiv:1503.06785] [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].
A. Achúcarro, R. Kallosh, A. Linde, D.-G. Wang and Y. Welling, Universality of multi-field α-attractors, JCAP04 (2018) 028 [arXiv:1711.09478] [INSPIRE].
Y. Akrami, R. Kallosh, A. Linde and V. Vardanyan, Dark energy, α-attractors and large-scale structure surveys, JCAP06 (2018) 041 [arXiv:1712.09693] [INSPIRE].
R. Schimmrigk, Automorphic inflation, Phys. Lett.B 748 (2015) 376 [arXiv:1412.8537] [INSPIRE].
R. Schimmrigk, A general framework of automorphic inflation, JHEP05 (2016) 140 [arXiv:1512.09082] [INSPIRE].
R. Schimmrigk, Modular inflation observables and j-inflation phenomenology, JHEP09 (2017) 043 [arXiv:1612.09559] [INSPIRE].
R. Schimmrigk, Multifield reheating after modular j-inflation, Phys. Lett.B 782 (2018) 193 [arXiv:1712.09961] [INSPIRE].
M. Lynker and R. Schimmrigk, Modular inflation at higher level N, JCAP06 (2019) 036 [arXiv:1902.04625] [INSPIRE].
S. Capozziello and R. de Ritis, Relation between the potential and nonminimal coupling in inflationary cosmology, Phys. Lett.A 177 (1993) 1 [INSPIRE].
P.J. Olver, Applications of Lie groups to differential equations, second edition, Grad. Texts Math.107, Springer, New York, U.S.A. (1998).
A. Linde, D.-G. Wang, Y. Welling, Y. Yamada and A. Achúcarro, Hypernatural inflation, JCAP07 (2018) 035 [arXiv:1803.09911] [INSPIRE].
M. Dias, J. Frazer, A. Retolaza, M. Scalisi and A. Westphal, Pole N -flation, JHEP02 (2019) 120 [arXiv:1805.02659] [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].
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, JCAP07 (2018) 057 [arXiv:1804.11279] [INSPIRE].
T. Bjorkmo, Rapid-turn inflationary attractors, Phys. Rev. Lett.122 (2019) 251301 [arXiv:1902.10529] [INSPIRE].
S. Capozziello and A. De Felice, f (R) cosmology by Noether’s symmetry, JCAP08 (2008) 016 [arXiv:0804.2163] [INSPIRE].
H. Motohashi, A.A. Starobinsky and J. Yokoyama, Inflation with a constant rate of roll, JCAP09 (2015) 018 [arXiv:1411.5021] [INSPIRE].
L. Anguelova, P. Suranyi and L.C.R. Wijewardhana, Systematics of constant roll inflation, JCAP02 (2018) 004 [arXiv:1710.06989] [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: 1905.01611
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
Anguelova, L., Babalic, E.M. & Lazaroiu, C.I. Hidden symmetries of two-field cosmological models. J. High Energ. Phys. 2019, 7 (2019). https://doi.org/10.1007/JHEP09(2019)007
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2019)007