Abstract
We study Noether symmetries in two-field cosmological α-attractors, investigating the case when the scalar manifold is an elementary hyperbolic surface. This encompasses and generalizes the case of the Poincaré disk. We solve the conditions for the existence of a ‘separated’ Noether symmetry and find the form of the scalar potential compatible with such, for any elementary hyperbolic surface. For this class of symmetries, we find that the α-parameter must have a fixed value. Using those Noether symmetries, we also obtain many exact solutions of the equations of motion of these models, which were studied previously with numerical methods.
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References
R. Kallosh, A. Linde and D. Roest, Superconformal inflationary α-attractors, JHEP 11 (2013) 198 [arXiv:1311.0472] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, Large field inflation and double α-attractors, JHEP 08 (2014) 052 [arXiv:1405.3646] [INSPIRE].
R. Kallosh and A. Linde, Universality class in conformal inflation, JCAP 07 (2013) 002 [arXiv:1306.5220] [INSPIRE].
R. Kallosh and A. Linde, Multi-field conformal cosmological attractors, JCAP 12 (2013) 006 [arXiv:1309.2015] [INSPIRE].
R. Kallosh and A. Linde, Escher in the sky, Comptes Rendus Physique 16 (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 et al., Universality of multi-field α-attractors, JCAP 04 (2018) 028 [arXiv:1711.09478] [INSPIRE].
A. Linde et al., Hypernatural inflation, JCAP 07 (2018) 035 [arXiv:1803.09911] [INSPIRE].
M. Dias et al., Pole N-flation, JHEP 02 (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, JCAP 07 (2018) 057 [arXiv:1804.11279] [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].
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].
W.H. Kinney, S. Vagnozzi and L. Visinelli, The zoo plot meets the swampland: mutual (in)consistency of single-field inflation, string conjectures and cosmological data, arXiv:1808.06424 [INSPIRE].
A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, JCAP 02 (2019) 041 [arXiv:1807.04390] [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].
M. Cicoli et al., De Sitter vs Quintessence in String Theory, Fortsch. Phys. 67 (2019) 1800079 [arXiv:1808.08967] [INSPIRE].
S. Kachru and S.P. Trivedi, A comment on effective field theories of flux vacua, Fortsch. Phys. 67 (2019) 1800086 [arXiv:1808.08971] [INSPIRE].
Y. Akrami, R. Kallosh, A. Linde and V. Vardanyan, The landscape, the swampland and the era of precision cosmology, Fortsch. Phys. 67 (2019) 1800075 [arXiv:1808.09440] [INSPIRE].
H. Murayama, M. Yamazaki and T.T. Yanagida, Do we live in the swampland?, JHEP 12 (2018) 032 [arXiv:1809.00478] [INSPIRE].
S. Capozziello and R. de Ritis, Relation between the potential and nonminimal coupling in inflationary cosmology, Phys. Lett. A 177 (1993) 1.
S. Capozziello, G. Marmo, C. Rubano and P. Scudellaro, Noether symmetries in Bianchi universes, Int. J. Mod. Phys. D 6 (1997) 491 [gr-qc/9606050] [INSPIRE].
S. Capozziello, S. Nesseris and L. Perivolaropoulos, Reconstruction of the scalar-tensor lagrangian from a LCDM background and Noether symmetry, JCAP 12 (2007) 009 [arXiv:0705.3586] [INSPIRE].
S. Capozziello and A. De Felice, f(R) cosmology by Noether’s symmetry, JCAP 08 (2008) 016 [arXiv:0804.2163] [INSPIRE].
N. Kaewkhao, T. Kanesom and P. Channuie, Noether symmetry approach in the cosmological alpha-attractors, Nucl. Phys. B 931 (2018) 216 [arXiv:1711.10080] [INSPIRE].
N. Bartolo et al., Supergravity, α-attractors and primordial non-Gaussianity, JCAP 10 (2018) 017 [arXiv:1805.04269] [INSPIRE].
Y. Akrami, R. Kallosh, A. Linde and V. Vardanyan, Dark energy, α-attractors and large-scale structure surveys, JCAP 06 (2018) 041 [arXiv:1712.09693] [INSPIRE].
J. Ellis, B. Nagaraj, D.V. Nanopoulos and K.A. Olive, De Sitter vacua in no-scale supergravity, JHEP 11 (2018) 110 [arXiv:1809.10114] [INSPIRE].
E. Cremmer, J. Scherk and S. Ferrara, SU(4) invariant supergravity theory, Phys. Lett. 74B (1978) 61 [INSPIRE].
E.M. Babalic and C.I. Lazaroiu, Cosmological flows on hyperbolic surfaces, arXiv:1810.00441 [INSPIRE].
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Anguelova, L., Babalic, E.M. & Lazaroiu, C.I. Two-field cosmological α-attractors with Noether symmetry. J. High Energ. Phys. 2019, 148 (2019). https://doi.org/10.1007/JHEP04(2019)148
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DOI: https://doi.org/10.1007/JHEP04(2019)148