Abstract
Recently, two simple criteria were proposed to assess if vacua emerging from an effective scalar field theory are part of the string “landscape” or “swampland”. The former are the vacua that emerge from string compactifications; the latter are not obtained by any such compactification and hence may not survive in a UV completed theory of gravity. So far, these criteria have been applied to inflationary and dark energy models. Here we consider them in the context of solitonic compact objects made up of scalar fields: boson stars. Analysing several models (static, rotating, with and without self-interactions), we find that, in this context, the criteria are not independent. Furthermore, we find the universal behaviour that in the region wherein the boson stars are expected to be perturbatively stable, the compact objects may be part of the landscape. By contrast, in the region where they may be faithful black hole mimickers, in the sense they possess a light ring, the criteria fail (are obeyed) for static (rotating) ultracompact boson stars, which should thus be part of the swampland (landscape). We also consider hairy black holes interpolating between these boson stars and the Kerr solution and establish the part of the domain of existence where the swampland criteria are violated. In interpreting these results one should bear in mind, however, that the swampland criteria are not quantitatively strict.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Supernova Search Team collaboration, Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201] [INSPIRE].
S. Perlmutter, M.S. Turner and M.J. White, Constraining dark energy with SNe Ia and large scale structure, Phys. Rev. Lett. 83 (1999) 670 [astro-ph/9901052] [INSPIRE].
WMAP collaboration, Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, Astrophys. J. Suppl. 208 (2013) 20 [arXiv:1212.5225] [INSPIRE].
Planck collaboration, Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE].
C. Blake and K. Glazebrook, Probing dark energy using baryonic oscillations in the galaxy power spectrum as a cosmological ruler, Astrophys. J. 594 (2003) 665 [astro-ph/0301632] [INSPIRE].
H.-J. Seo and D.J. Eisenstein, Probing dark energy with baryonic acoustic oscillations from future large galaxy redshift surveys, Astrophys. J. 598 (2003) 720 [astro-ph/0307460] [INSPIRE].
S.D.M. White, J.F. Navarro, A.E. Evrard and C.S. Frenk, The baryon content of galaxy clusters: A challenge to cosmological orthodoxy, Nature 366 (1993) 429 [INSPIRE].
P. Schuecker, H. Bohringer, C.A. Collins and L. Guzzo, The REFLEX galaxy cluster survey VII: Ωm and σ 8 from cluster abundance and large scale clustering, Astron. Astrophys. 398 (2003) 867 [astro-ph/0208251] [INSPIRE].
M. Kilbinger et al., Dark energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5, Astron. Astrophys. 497 (2009) 677 [arXiv:0810.5129] [INSPIRE].
D.M. Scolnic et al., The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample, Astrophys. J. 859 (2018) 101 [arXiv:1710.00845] [INSPIRE].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [INSPIRE].
BICEP2 and Keck Array collaborations, BICEP2/Keck Array V: Measurements of B-mode Polarization at Degree Angular Scales and 150 GHz by the Keck Array, Astrophys. J. 811 (2015) 126 [arXiv:1502.00643] [INSPIRE].
M. Graña, Flux compactifications in string theory: A comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].
R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477] [hep-th/9906070] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
S. Kachru, M.B. Schulz and S. Trivedi, Moduli stabilization from fluxes in a simple IIB orientifold, JHEP 10 (2003) 007 [hep-th/0201028] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister and S.P. Trivedi, Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
H. Kodama and K. Uzawa, Moduli instability in warped compactifications of the type IIB supergravity, JHEP 07 (2005) 061 [hep-th/0504193] [INSPIRE].
O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].
H. Kodama and K. Uzawa, Comments on the four-dimensional effective theory for warped compactification, JHEP 03 (2006) 053 [hep-th/0512104] [INSPIRE].
B. de Wit, D.J. Smit and N.D. Hari Dass, Residual Supersymmetry of Compactified D = 10 Supergravity, Nucl. Phys. B 283 (1987) 165 [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
S. Ivanov and G. Papadopoulos, A no go theorem for string warped compactifications, Phys. Lett. B 497 (2001) 309 [hep-th/0008232] [INSPIRE].
N. Goheer, M. Kleban and L. Susskind, The trouble with de Sitter space, JHEP 07 (2003) 056 [hep-th/0212209] [INSPIRE].
M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary Constraints on Type IIA String Theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [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].
L. Susskind, The anthropic landscape of string theory, hep-th/0302219 [INSPIRE].
T. Banks, M. Dine and E. Gorbatov, Is there a string theory landscape?, JHEP 08 (2004) 058 [hep-th/0309170] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [INSPIRE].
R. Kallosh and A.D. Linde, Landscape, the scale of SUSY breaking and inflation, JHEP 12 (2004) 004 [hep-th/0411011] [INSPIRE].
C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
F. Denef, Les Houches Lectures on Constructing String Vacua, Les Houches 87 (2008) 483 [arXiv:0803.1194] [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland and the Missing Corner, PoS(TASI2017)015 (2017) [arXiv:1711.00864] [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].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [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].
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].
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].
R. Blumenhagen, I. Valenzuela and F. Wolf, The Swampland Conjecture and F-term Axion Monodromy Inflation, JHEP 07 (2017) 145 [arXiv:1703.05776] [INSPIRE].
A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, arXiv:1807.04390 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, arXiv:1807.05193 [INSPIRE].
A. Kehagias and A. Riotto, A note on Inflation and the Swampland, Fortsch. Phys. 66 (2018) 100052 [arXiv:1807.05445] [INSPIRE].
H. Matsui and F. Takahashi, Eternal Inflation and Swampland Conjectures, arXiv:1807.11938 [INSPIRE].
C. Damian and O. Loaiza-Brito, Two-field axion inflation and the swampland constraint in the flux-scaling scenario, arXiv:1808.03397 [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].
S. Brahma and M. Wali Hossain, Avoiding the string swampland in single-field inflation: Excited initial states, arXiv:1809.01277 [INSPIRE].
C. Han, S. Pi and M. Sasaki, Quintessence Saves Higgs Instability, arXiv:1809.05507 [INSPIRE].
K. Dimopoulos, Steep Eternal Inflation and the Swampland, Phys. Rev. D 98 (2018) 123516 [arXiv:1810.03438] [INSPIRE].
C.-M. Lin, K.-W. Ng and K. Cheung, Chaotic inflation on the brane and the Swampland Criteria, arXiv:1810.01644 [INSPIRE].
A. Ashoorioon, Rescuing Single Field Inflation from the Swampland, arXiv:1810.04001 [INSPIRE].
S. Das, Warm Inflation in the light of Swampland Criteria, arXiv:1810.05038 [INSPIRE].
S.-J. Wang, Quintessential Starobinsky inflation and swampland criteria, arXiv:1810.06445 [INSPIRE].
S.K. Garg, C. Krishnan and M. Zaid, Bounds on Slow Roll at the Boundary of the Landscape, arXiv:1810.09406 [INSPIRE].
J.J. Heckman, C. Lawrie, L. Lin and G. Zoccarato, F-theory and Dark Energy, arXiv:1811.01959 [INSPIRE].
C.-I. Chiang, J.M. Leedom and H. Murayama, What does Inflation say about Dark Energy given the Swampland Conjectures?, arXiv:1811.01987 [INSPIRE].
F.E. Schunck and E.W. Mielke, General relativistic boson stars, Class. Quant. Grav. 20 (2003) R301 [arXiv:0801.0307] [INSPIRE].
S.L. Liebling and C. Palenzuela, Dynamical Boson Stars, Living Rev. Rel. 15 (2012) 6 [arXiv:1202.5809] [INSPIRE].
D.J. Kaup, Klein-Gordon Geon, Phys. Rev. 172 (1968) 1331 [INSPIRE].
R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of an equation of state, Phys. Rev. 187 (1969) 1767 [INSPIRE].
E. Seidel and W.-M. Suen, Formation of solitonic stars through gravitational cooling, Phys. Rev. Lett. 72 (1994) 2516 [gr-qc/9309015] [INSPIRE].
P. Jetzer, Dynamical Instability of Bosonic Stellar Configurations, Nucl. Phys. B 316 (1989) 411 [INSPIRE].
M. Gleiser and R. Watkins, Gravitational Stability of Scalar Matter, Nucl. Phys. B 319 (1989) 733 [INSPIRE].
T.D. Lee and Y. Pang, Stability of Mini-Boson Stars, Nucl. Phys. B 315 (1989) 477 [INSPIRE].
F.S. Guzman and J.M. Rueda-Becerril, Spherical boson stars as black hole mimickers, Phys. Rev. D 80 (2009) 084023 [arXiv:1009.1250] [INSPIRE].
F.H. Vincent, Z. Meliani, P. Grandclement, E. Gourgoulhon and O. Straub, Imaging a boson star at the Galactic center, Class. Quant. Grav. 33 (2016) 105015 [arXiv:1510.04170] [INSPIRE].
P.V.P. Cunha, J.A. Font, C. Herdeiro, E. Radu, N. Sanchis-Gual and M. Zilhão, Lensing and dynamics of ultracompact bosonic stars, Phys. Rev. D 96 (2017) 104040 [arXiv:1709.06118] [INSPIRE].
A. Suárez, V.H. Robles and T. Matos, A Review on the Scalar Field/Bose-Einstein Condensate Dark Matter Model, Astrophys. Space Sci. Proc. 38 (2014) 107 [arXiv:1302.0903] [INSPIRE].
S. Krippendorf, F. Muia and F. Quevedo, Moduli Stars, JHEP 08 (2018) 070 [arXiv:1806.04690] [INSPIRE].
B. Li, T. Rindler-Daller and P.R. Shapiro, Cosmological Constraints on Bose-Einstein-Condensed Scalar Field Dark Matter, Phys. Rev. D 89 (2014) 083536 [arXiv:1310.6061] [INSPIRE].
F.E. Schunck and E.W. Mielke, Rotating boson star as an effective mass torus in general relativity, Phys. Lett. A 249 (1998) 389 [INSPIRE].
S. Yoshida and Y. Eriguchi, Rotating boson stars in general relativity, Phys. Rev. D 56 (1997) 762 [INSPIRE].
C.A.R. Herdeiro and E. Radu, Kerr black holes with scalar hair, Phys. Rev. Lett. 112 (2014) 221101 [arXiv:1403.2757] [INSPIRE].
C. Herdeiro and E. Radu, Construction and physical properties of Kerr black holes with scalar hair, Class. Quant. Grav. 32 (2015) 144001 [arXiv:1501.04319] [INSPIRE].
R.P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11 (1963) 237 [INSPIRE].
M. Colpi, S.L. Shapiro and I. Wasserman, Boson Stars: Gravitational Equilibria of Selfinteracting Scalar Fields, Phys. Rev. Lett. 57 (1986) 2485 [INSPIRE].
V. Cardoso, E. Franzin and P. Pani, Is the gravitational-wave ringdown a probe of the event horizon?, Phys. Rev. Lett. 116 (2016) 171101 [Erratum ibid. 117 (2016) 089902] [arXiv:1602.07309] [INSPIRE].
P.V.P. Cunha, E. Berti and C.A.R. Herdeiro, Light-Ring Stability for Ultracompact Objects, Phys. Rev. Lett. 119 (2017) 251102 [arXiv:1708.04211] [INSPIRE].
K. Dasgupta, M. Emelin, E. McDonough and R. Tatar, Quantum Corrections and the de Sitter Swampland Conjecture, JHEP 01 (2019) 145 [arXiv:1808.07498] [INSPIRE].
U. Danielsson, The quantum swampland, arXiv:1809.04512 [INSPIRE].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].
R. Blumenhagen, Large Field Inflation/Quintessence and the Refined Swampland Distance Conjecture, PoS(CORFU2017)175 (2018) [arXiv:1804.10504] [INSPIRE].
D. Andriot and C. Roupec, Further refining the de Sitter swampland conjecture, arXiv:1811.08889 [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].
J.P. Conlon, The de Sitter swampland conjecture and supersymmetric AdS vacua, Int. J. Mod. Phys. A 33 (2018) 1850178 [arXiv:1808.05040] [INSPIRE].
H. Murayama, M. Yamazaki and T.T. Yanagida, Do We Live in the Swampland?, JHEP 12 (2018) 032 [arXiv:1809.00478] [INSPIRE].
K. Choi, D. Chway and C.S. Shin, The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking, JHEP 11 (2018) 142 [arXiv:1809.01475] [INSPIRE].
K. Hamaguchi, M. Ibe and T. Moroi, The swampland conjecture and the Higgs expectation value, JHEP 12 (2018) 023 [arXiv:1810.02095] [INSPIRE].
M. Emelin and R. Tatar, Axion Hilltops, Kähler Modulus Quintessence and the Swampland Criteria, arXiv:1811.07378 [INSPIRE].
J. Blåbäck, U. Danielsson and G. Dibitetto, A new light on the darkest corner of the landscape, arXiv:1810.11365 [INSPIRE].
A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].
C.A.R. Herdeiro, E. Radu and H. Rúnarsson, Kerr black holes with self-interacting scalar hair: hairier but not heavier, Phys. Rev. D 92 (2015) 084059 [arXiv:1509.02923] [INSPIRE].
G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles, J. Math. Phys. 5 (1964) 1252 [INSPIRE].
J. Balakrishna, E. Seidel and W.-M. Suen, Dynamical evolution of boson stars. 2. Excited states and selfinteracting fields, Phys. Rev. D 58 (1998) 104004 [gr-qc/9712064] [INSPIRE].
C.A.R. Herdeiro, E. Radu and H.F. Rúnarsson, Spinning boson stars and Kerr black holes with scalar hair: the effect of self-interactions, Int. J. Mod. Phys. D 25 (2016) 1641014 [arXiv:1604.06202] [INSPIRE].
P.V.P. Cunha, C.A.R. Herdeiro, E. Radu and H.F. Runarsson, Shadows of Kerr black holes with scalar hair, Phys. Rev. Lett. 115 (2015) 211102 [arXiv:1509.00021] [INSPIRE].
C.A.R. Herdeiro and E. Radu, Asymptotically flat black holes with scalar hair: a review, Int. J. Mod. Phys. D 24 (2015) 1542014 [arXiv:1504.08209] [INSPIRE].
S. Hod, Stationary Scalar Clouds Around Rotating Black Holes, Phys. Rev. D 86 (2012) 104026 [Erratum ibid. D 86 (2012) 129902] [arXiv:1211.3202] [INSPIRE].
S. Hod, Stationary resonances of rapidly-rotating Kerr black holes, Eur. Phys. J. C 73 (2013) 2378 [arXiv:1311.5298] [INSPIRE].
S. Hod, Kerr-Newman black holes with stationary charged scalar clouds, Phys. Rev. D 90 (2014) 024051 [arXiv:1406.1179] [INSPIRE].
C.L. Benone, L.C.B. Crispino, C. Herdeiro and E. Radu, Kerr-Newman scalar clouds, Phys. Rev. D 90 (2014) 104024 [arXiv:1409.1593] [INSPIRE].
S. Hod, Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime, JHEP 01 (2017) 030 [arXiv:1612.00014] [INSPIRE].
J.C. Degollado, C.A.R. Herdeiro and E. Radu, Effective stability against superradiance of Kerr black holes with synchronised hair, Phys. Lett. B 781 (2018) 651 [arXiv:1802.07266] [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: 1811.10844
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
Herdeiro, C.A.R., Radu, E. & Uzawa, K. Compact objects and the swampland. J. High Energ. Phys. 2019, 215 (2019). https://doi.org/10.1007/JHEP01(2019)215
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)215