Abstract
This is a short summary of lectures on some of the recent ideas emerging in the discussion of quantum gravity with a positive cosmological constant. The lectures given at the School on Quantum Gravity, at Centro de Estudios Científicos, Valdivia, Chile in January 2002. The following summary is largely based on material appearing in refs. [1, 2, 3].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Bousso, O. DeWolfe and R.C. Myers, “Unbounded entropy in spacetimes with positive cosmological constant,” arXiv:hep-th/0205080.
F. Leblond, D. Marolf and R.C. Myers, “Tall tales from de Sitter space I: Renormalization group flows,” JHEP 0206 (2002) 052 [arXiv:hep-th/0202094].
F. Leblond, D. Marolf and R.C. Myers, “Tall tales from de Sitter space II: Field theory dualities,” [arXiv:hep-th/0211025].
S. Perlmutter et al. [Supernova Cosmology Project Collaboration], “Measurements of the Cosmological Parameters Ω and Λ from the First Seven Supernovae at z≥35,” Astrophys. J. 483, 565 (1997) [arXiv:astro-ph/9608192]; S. Perlmutter et al. [Supernova Cosmology Project Collaboration], “Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications,” Nature 391, 51 (1998) [arXiv:astro-ph/9712212]; A.G. Riess et al. [Supernova Search Team Collaboration], “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,” Astron. J. 116, 1009 (1998) [arXiv:astro-ph/9805201].; N.A. Bahcall, J.P. Ostriker, S. Perlmutter and P.J. Steinhardt, “The Cosmic Triangle: Revealing the State of the Universe,” Science 284, 1481 (1999) [arXiv:astro-ph/9906463]; P. de Bernardis et al., “Multiple peaks in the angular power spectrum of the cosmic microwave background: Significance and consequences for cosmology,” Astrophys. J. 564 (2002) 559 [arXiv:astro-ph/0105296]; R. Stompor et al., “Cosmological implications of the MAXIMA-I high resolution Cosmic Microwave Background anisotropy measurement,” Astrophys. J. 561 (2001) L7 [arXiv:astro-ph/0105062]; A.H. Jaffe et al. [Boomerang Collaboration], “Cosmology from Maxima-1, Boomerang and COBE/DMR CMB Observations,” Phys. Rev. Lett. 86 (2001) 3475 [arXiv:astroph/0007333]; M.E. Abroe et al., “Frequentist Estimation of Cosmological Parameters from the MAXIMA-1 Cosmic Microwave Background Anisotropy Data,” Mon. Not. Roy. Astron. Soc. 334 (2002) 11 [arXiv:astro-ph/0111010].
A. Strominger, “The dS/CFT correspondence,” JHEP 0110 (2001) 034 [arXiv:hep-th/0106113].
E. Witten, “Quantum gravity in de Sitter space,” arXiv:hep-th/0106109.
T. Banks, “Cosmological breaking of supersymmetry or little Lambda goes back to the future. II,” arXiv:hep-th/0007146.
W. Fischler, “Taking de Sitter seriously,” talk given at Role of Scaling Laws in Physics and Biology (Celebrating the 60th Birthday of Geoffrey West), Santa Fe, December 2000.
A. Strominger, “Inflation and the dS/CFT correspondence,” JHEP 0111 (2001) 049 [arXiv:hep-th/0110087].
V. Balasubramanian, J. de Boer, and D. Minic, “Mass, Entropy, and Holography in Asymptotically de Sitter spaces” Phys. Rev. D 65 (2002) 123508 [arXiv:hep-th/0110108].
R. Bousso, A. Maloney and A. Strominger, “Conformal vacua and entropy in de Sitter space,” Phys. Rev. D 65 (2002) 104039 [arXiv:hep-th/0112218].
M. Spradlin and A. Volovich, “Vacuum states and the S-matrix in dS/CFT,” Phys. Rev. D 65 (2002) 104037 [arXiv:hep-th/0112223].
V. Balasubramanian, P. Horava, and D. Minic, “Deconstructing De Sitter,” JHEP 0105 (2001) 043 [arXiv:hep-th/0103171].
A.M. Ghezelbash and R.B. Mann, “Action, mass and entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT correspondence,” JHEP 0201 (2002) 005 [arXiv:hep-th/0111217].
D. Klemm and L. Vanzo, “De Sitter gravity and Liouville theory,” JHEP 0204 (2002) 030 [arXiv:hep-th/0203268].
D. Klemm, “Some aspects of the de Sitter/CFT correspondence,” Nucl. Phys. B 625 (2002) 295 [arXiv:hep-th/0106247]; S. Cacciatori and D. Klemm, “The asymptotic dynamics of de Sitter gravity in three dimensions,” Class. Quant. Grav. 19 (2002) 579 [arXiv:hep-th/0110031].
M.K. Parikh, I. Savonije and E. Verlinde, “Elliptic de Sitter space: dS/Z(2),” arXiv:hep-th/0209120.
G.W. Gibbons and S. Hawking, “Cosmological event horizons, thermodynamics and particle creation,” Phys. Rev. D 7 (1977) 2738.
A. Strominger and C. Vafa, “Microscopic Origin of the Bekenstein-Hawking Entropy,” Phys. Lett. B 379 (1996) 99 [arXiv:hep-th/9601029].
A.W. Peet, “TASI lectures on black holes in string theory,” arXiv:hep-th/0008241; S.R. Das and S.D. Mathur, “The Quantum Physics Of Black Holes: Results From String Theory,” Ann. Rev. Nucl. Part. Sci. 50 (2000) 153 [arXiv:gr-qc/0105063]; J.R. David, G. Mandal and S.R. Wadia, “Microscopic formulation of black holes in string theory,” Phys. Rept. 369 (2002) 549 [arXiv:hep-th/0203048].
J.M. Maldacena, “Black holes in string theory,” arXiv:hep-th/9607235.
R.C. Myers, “Black holes and string theory,” arXiv:gr-qc/0107034.
C.V. Johnson, D-branes (Cambridge University Press, 2002).
R.C. Myers, “Nonabelian D-branes and noncommutative geometry,” Int. J. Mod. Phys. A 16 (2001) 956 [arXiv:hep-th/0106178].
R.C. Myers, “Dielectric-branes,” JHEP 9912 (1999) 022 [arXiv:hep-th/9910053].
http://www.hasd.org/ges/talltale/talltale.htm
See, for example: S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time (Cambridge: Cambridge University Press, 1980).
J.D. Bekenstein, “Generalized Second Law Of Thermodynamics In Black Hole Physics,” Phys. Rev. D 9 (1974) 3292; J.D. Bekenstein, “Black Holes And Entropy,” Phys. Rev. D 7 (1973) 2333; J.D. Bekenstein, “Black Holes And The Second Law,” Lett. Nuovo Cim. 4 (1972) 737.
S. Hawking, J.M. Maldacena and A. Strominger, “DeSitter entropy, quantum entanglement and AdS/CFT,” JHEP 0105 (2001) 001 [arXiv:hep-th/0002145].
S. Carlip, Quantum Gravity In 2+1 Dimensions, (Cambridge University Press, 1998).
J.M. Maldacena and A. Strominger, “Statistical entropy of de Sitter space,” JHEP 9802 (1998) 014 [arXiv:gr-qc/9801096]; F.L. Lin and Y.S. Wu, “Near-horizon Virasoro symmetry and the entropy of de Sitter space in any dimension,” Phys. Lett. B 453 (1999) 222 [arXiv:hep-th/9901147].
L. Smolin, “Quantum gravity with a positive cosmological constant,” arXiv:hep-th/0209079.
G. ’t Hooft, “Dimensional Reduction In Quantum Gravity,” arXiv:gr-qc/9310026; L. Susskind, “The World as a hologram,” J. Math. Phys. 36 (1995) 6377 [arXiv:hep-th/9409089].
R. Bousso, “Holography in general space-times,” JHEP 9906, 028 (1999) [arXiv:hep-th/9906022]; “A Covariant Entropy Conjecture,” JHEP 9907, 004 (1999) [arXiv:hep-th/9905177].
R. Bousso, “The holographic principle,” Rev. Mod. Phys. 74 (2002) 825 [arXiv:hep-th/0203101].
R. Bousso, “Bekenstein bounds in de Sitter and flat space,” JHEP 0104 (2001) 035 [arXiv:hep-th/0012052].
L. Susskind, L. Thorlacius and J. Uglum, “The Stretched horizon and black hole complementarity,” Phys. Rev. D 48, 3743 (1993) [arXiv:hep-th/9306069]; L. Susskind, “String theory and the principles of black hole complementarity,” Phys. Rev. Lett. 71, 2367 (1993) [arXiv:hep-th/9307168]; L. Susskind and L. Thorlacius, “Gedanken experiments involving black holes,” Phys. Rev. D 49, 966 (1994) [arXiv:hep-th/9308100].
R. Bousso, “Positive vacuum energy and the N-bound,” JHEP 0011 (2000) 038 [arXiv:hep-th/0010252].
P.G. Freund and M.A. Rubin, “Dynamics Of Dimensional Reduction,” Phys. Lett. B 97 (1980) 233.
E. Silverstein, “(A)dS backgrounds from asymmetric orientifolds,” arXiv:hep-th/0106209; A. Maloney, E. Silverstein and A. Strominger, “De Sitter space in noncritical string theory,” arXiv:hep-th/0205316.
C.M. Hull, “De Sitter space in supergravity and M theory,” JHEP 0111 (2001) 012 [arXiv:hep-th/0109213]; C.M. Hull, “Domain wall and de Sitter solutions of gauged supergravity,” JHEP 0111 (2001) 061 [arXiv:hep-th/0110048]; G.W. Gibbons and C.M. Hull, “de Sitter space from warped supergravity solutions,” arXiv:hep-th/0111072.
M. Gutperle and A. Strominger, “Spacelike branes,” JHEP 0204 (2002) 018 [arXiv:hep-th/0202210]; C.M. Chen, D.V. Gal’tsov and M. Gutperle, “S-brane solutions in supergravity theories,” Phys. Rev. D 66 (2002) 024043 [arXiv:hep-th/0204071]; M. Kruczenski, R.C. Myers and A.W. Peet, “Supergravity S-branes,” JHEP 0205 (2002) 039 [arXiv:hep-th/0204144].
C. Herdeiro, S. Hirano and R. Kallosh, “String theory and hybrid inflation / acceleration,” JHEP 0112 (2001) 027 [arXiv:hep-th/0110271]; K. Dasgupta, C. Herdeiro, S. Hirano and R. Kallosh, “D3/D7 inflationary model and M-theory,” Phys. Rev. D 65 (2002) 126002 [arXiv:hep-th/0203019].
J.D. Brown and C. Teitelboim, “Neutralization Of The Cosmological Constant By Membrane Creation,” Nucl. Phys. B 297 (1988) 787; J.D. Brown and C. Teitelboim, “Dynamical Neutralization Of The Cosmological Constant,” Phys. Lett. B 195 (1987) 177.
T. Banks, “Heretics of the false vacuum: Gravitational effects on and of vacuum decay. II,” arXiv:hep-th/0211160.
O. Aharony, S.S. Gubser, J. Maldacena, H. Ooguri and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept. 323, 183 (2000) [arXiv:hep-th/9905111].
V. Balasubramanian, J. de Boer and D. Minic, “Exploring de Sitter space and holography,” arXiv:hep-th/0207245; to appear in Annals of Physics.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2 (1998) 253 [arXiv:hep-th/9802150].
V. Balasubramanian, P. Kraus and A.E. Lawrence, “Bulk vs. boundary dynamics in anti-de Sitter spacetime,” Phys. Rev. D 59 (1999) 046003 [arXiv:hep-th/9805171].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428 (1998) 105 [arXiv:hep-th/9802109].
P. Breitenlohner and D.Z. Freedman, “Positive Energy In Anti-De Sitter Backgrounds And Gauged Extended Supergravity,” Phys. Lett. B 115 (1982) 197; “Stability In Gauged Extended Supergravity,” Annals Phys. 144 (1982) 249.
L. Mezincescu and P.K. Townsend, “Stability At A Local Maximum In Higher Dimensional Anti-De Sitter Space And Applications To Supergravity,” Annals Phys. 160 (1985) 406.
I.R. Klebanov and E. Witten, “AdS/CFT correspondence and symmetry breaking,” Nucl. Phys. B 556 (1999) 89 [arXiv:hep-th/9905104].
L. Susskind and E. Witten, “The holographic bound in anti-de Sitter space,” arXiv:hep-th/9805114; A.W. Peet and J. Polchinski, “UV/IR relations in AdS dynamics,” Phys. Rev. D 59, 065011 (1999) [arXiv:hep-th/9809022].
R. Emparan, C.V. Johnson and R.C. Myers, “Surface terms as counterterms in the AdS/CFT correspondence,” Phys. Rev. D 60, 104001 (1999) [arXiv:hep-th/9903238].
V. Balasubramanian and P. Kraus, “Spacetime and the holographic renormalization group,” Phys. Rev. Lett. 83 (1999) 3605 [arXiv:hep-th/9903190].
N.R. Constable and R.C. Myers, “Exotic scalar states in the AdS/CFT correspondence,” JHEP 9911, 020 (1999) [arXiv:hep-th/9905081]; K.A. Intriligator, “Maximally supersymmetric RG flows and AdS duality,” Nucl. Phys. B 580, 99 (2000) [arXiv:hep-th/9909082]; M.S. Costa, “Absorption by double-centered D3-branes and the Coulomb branch of N=4 SYM theory,” JHEP 0005, 041 (2000) [arXiv:hep-th/9912073]; M.S. Costa, “A test of the AdS/CFT duality on the Coulomb branch,” Phys. Lett. B 482, 287 (2000) [Erratum-ibid. B 489, 439 (2000)] [arXiv:hep-th/0003289]; U.H. Danielsson, A. Guijosa, M. Kruczenski and B. Sundborg, “D3-brane holography,” JHEP 0005, 028 (2000) [arXiv:hep-th/0004187]; N. Evans, C.V. Johnson and M. Petrini, “Clearing the throat: Irrelevant operators and finite temperature in large N gauge theory,” JHEP 0205, 002 (2002) [arXiv:hep-th/0112058].
J. Distler and F. Zamora, “Non-supersymmetric conformal field theories from stable anti-de Sitter spaces,” Adv. Theor. Math. Phys. 2, 1405 (1999) [arXiv:hep-th/9810206]; L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, “Novel local CFT and exact results on perturbations of N=4 super Yang-Mills from AdS dynamics,” JHEP 9812, 022 (1998) [arXiv:hep-th/9810126]; D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, “Continuous distributions of D3-branes and gauged supergravity,” JHEP 0007, 038 (2000) [arXiv:hep-th/9906194]; N.R. Constable and R.C. Myers, “Exotic scalar states in the AdS/CFT correspondence,” JHEP 9911, 020 (1999) [arXiv:hep-th/9905081]; L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, “The supergravity dual of N = 1 super Yang-Mills theory,” Nucl. Phys. B 569, 451 (2000) [arXiv:hep-th/9909047].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, “Renormalization group flows from holography supersymmetry and a c-theorem,” Adv. Theor. Math. Phys. 3, 363 (1999) [arXiv:hep-th/9904017]; J. de Boer, E. Verlinde and H. Verlinde, “On the holographic renormalization group,” JHEP 0008, 003 (2000) [arXiv:hep-th/9912012]; V. Balasubramanian, E.G. Gimon and D. Minic, “Consistency conditions for holographic duality,” JHEP 0005, 014 (2000) [arXiv:hep-th/0003147]; V. Sahakian, “Holography, a covariant c-function and the geometry of the renormalization group,” Phys. Rev. D 62, 126011 (2000) [arXiv:hep-th/9910099]; E. Alvarez and C. Gomez, “Geometric holography, the renormalization group and the c-theorem,” Nucl. Phys. B 541, 441 (1999) [arXiv:hep-th/9807226].
See, for example: N.D. Birrell and P.C.W. Davies, Quantum fields in curved space (Cambridge, 1982).
E.A. Tagirov, “Consequences Of Field Quantization In De Sitter Type Cosmological Models,” Annals Phys. 76 (1973) 561.
R. Raczka, N. Limic and J. Niederle, “Discrete Degenerate Representations of Noncompact Rotation Groups. I,” J. Math. Phys. 7 (1966) 1861; N. Limic, J. Niederle and R. Raczka, J. Math. Phys. 8 (1966) 2026; N. Limic, J. Niederle and R. Raczka, “Eigenfunction Expansions Associated with the Second-Order Invariant Operator on Hyperboloids and Cones. III,” J. Math. Phys. 8 (1967) 1079.
B. Allen and A. Folacci, “The Massless Minimally Coupled Scalar Field In De Sitter Space,” Phys. Rev. D 35 (1987) 3771.
E. Mottola, “Particle Creation In De Sitter Space,” Phys. Rev. D 31 (1985) 754.
B. Allen, “Vacuum States In De Sitter Space,” Phys. Rev. D 32 (1985) 3136.
M. Spradlin and A. Volovich, “Vacuum states and the S-matrix in dS/CFT,” Phys. Rev. D 65 (2002) 104037 [arXiv:hep-th/0112223]. [rgflows] K.R. Kristjansson and L. Thorlacius, “Cosmological models and renormalization group flow,” JHEP 0205 (2002) 011 [arXiv:hep-th/0204058]; E. Halyo, “Holographic inflation,” arXiv:hep-th/0203235; A.J. Medved, “How not to construct an asymptotically de Sitter universe,” Class. Quant. Grav. 19 (2002) 4511 [arXiv:hep-th/0203191]; A.J. Medved, “dS-holographic C-functions with a topological, dilatonic twist,” Phys. Rev. D 66 (2002) 064001 [arXiv:hep-th/0202193]; R. Argurio, “Comments on cosmological RG flows,” arXiv:hep-th/0202183; F. Larsen, J.P. van der Schaar and R.G. Leigh, “de Sitter holography and the cosmic microwave background,” JHEP 0204 (2002) 047 [arXiv:hep-th/0202127].
A.B. Zamolodchikov, “Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory,” JETP Lett. 43, 730 (1986) [Pisma Zh. Eksp. Teor. Fiz. 43, 565 (1986)].
S. Gao and R.M. Wald, “The physical process version of the first law and the generalized second law for charged and rotating black holes,” Phys. Rev. D 64 (2001) 084020 [arXiv:gr-qc/0106071].
A. Borde and A. Vilenkin, “Eternal Inflation And The Initial Singularity,” Phys. Rev. Lett. 72 (1994) 3305 [arXiv:gr-qc/9312022]; A. Borde and A. Vilenkin, “The Impossibility Of Steady State Inflation,” arXiv:gr-qc/9403004; A. Borde and A. Vilenkin, “Singularities in inflationary cosmology: A review,” Int. J. Mod. Phys. D 5 (1996) 813 [arXiv:gr-qc/9612036]; A. Borde, A.H. Guth and A. Vilenkin, “Inflation is not past-eternal,” arXiv:gr-qc/0110012.
T. Vachaspati and M. Trodden, “Causality and cosmic inflation,” Phys. Rev. D 61 (2000) 023502 [arXiv:gr-qc/9811037].
A. Strominger, private communication.
J.M. Maldacena, “Eternal black holes in Anti-de-Sitter,” [arXiv:hep-th/0106112].
V. Balasubramanian, P. Kraus and A.E. Lawrence, “Bulk vs. boundary dynamics in anti-de Sitter spacetime,” Phys. Rev. D 59 (1999) 046003 [arXiv:hep-th/9805171].
J. Louko and D. Marolf, “Single-exterior black holes and the AdS-CFT conjecture,” Phys. Rev. D 59 (1999) 066002 [arXiv:hep-th/9808081].
G.J. Galloway, K. Schleich, D. Witt and E. Woolgar, “The AdS/CFT correspondence conjecture and topological censorship,” Phys. Lett. B 505 (2001) 255 [arXiv:hep-th/9912119]; “Topological censorship and higher genus black holes,” Phys. Rev. D 60 (1999) 104039 [arXiv:gr-qc/9902061].
M. Spradlin, A. Strominger and A. Volovich, “Les Houches lectures on de Sitter space,” arXiv:hep-th/0110007.
For example, the required flat space Green’s functions may be found in section 3 of: D.V. Galtsov, “Radiation reaction in various dimensions,” Phys. Rev. D 66 (2002) 025016 [arXiv:hep-th/0112110].
L. Dyson, J. Lindesay and L. Susskind, “Is there really a de Sitter/CFT duality,” JHEP 0208 (2002) 045 [arXiv:hep-th/0202163].
L. Dyson, M. Kleban and L. Susskind, “Disturbing implications of a cosmological constant,” JHEP 0210 (2002) 011 [arXiv:hep-th/0208013].
T. Banks, W. Fischler and S. Paban, “Recurrent nightmares?: Measurement theory in de Sitter space,” arXiv:hep-th/0210160.
J.P. Gazeau and M.V. Takook, “Massive vector field in de Sitter space,” J. Math. Phys. 41 (2000) 5920 [arXiv:gr-qc/9912080].
J. Mickelsson and J. Niederle, “Contractions of representations of de Sitter groups,” Commun. Math. Phys. 27 (1972) 167.
J.P. Gazeau, J. Renaud and M.V. Takook, “Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space,” Class. Quant. Grav. 17 (2000) 1415 [arXiv:gr-qc/9904023].
A.J. Tolley and N. Turok, “Quantization of the massless minimally coupled scalar field and the dS/CFT correspondence,” arXiv:hep-th/0108119.
M. Milton and I.A. Abramowitz, Handbook of mathematical functions (Dover, 1965).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Myers, R.C. (2005). Tall Tales from de Sitter Space. In: Gomberoff, A., Marolf, D. (eds) Lectures on Quantum Gravity. Series of the Centro De Estudios Científicos. Springer, Boston, MA. https://doi.org/10.1007/0-387-24992-3_6
Download citation
DOI: https://doi.org/10.1007/0-387-24992-3_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23995-8
Online ISBN: 978-0-387-24992-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)