Brane-world cosmology in higher derivative gravity or warped compactification in the next-to-leading order of AdS/CFT correspondence

Journal of High Energy Physics

Volumn 4, Issue 7 PART B, 2000, Pages 1-20

  Nojiri, Shin'ichi ^a   Odintsov, Sergei D ^b,c  

^a NATIONAL DEFENSE ACADEMY   (Japan)

^b UNIVERSITY OF GUANAJUATO   (Mexico)

^c TOMSK STATE PEDAGOGICAL UNIVERSITY   (Russian Federation)

Author keywords

AdS CFT Correspondance; D branes; Superstrings and Heterotic Strings

Indexed keywords

EID: 6944235320     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/07/049     Document Type: Article

References (51)

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6. H.A. Chamblin and H.S. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225]; N. Kaloper, Bent domain walls as braneworlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210]; A. Lukas, B.A. Ovrut and D. Waldram, Boundary inflation, Phys. Rev. D 61 (2000) 023506 [hep-th/9902071]; T. Nihei, Inflation in the five-dimensional universe with an orbifold extra dimension, Phys. Lett. B 465 (1999) 81 [hep-ph/9905487]; H.B. Kim and H.D. Kim, Inflation and gauge hierarchy in Randall-Sundrum compactification, Phys. Rev. D 61 (2000) 064003 [hep-th/9909053]; D.J. H. Chung and K. Freese, Cosmological challenges in theories with extra dimensions and remarks on the horizon problem, Phys. Rev. D 61 (2000) 023511 [hep-ph/9906542]; J. Garriga and M. Sasaki, Brane-world creation and black holes, Phys. Rev. D 62 (2000) 043523 [hep-th/9912118]; J.E. Kim and B. Kyae, Exact cosmological solution and modulus stabilization in the Randall-Sundrum model with bulk matter, Phys. Lett. B 486 (2000) 165 [hep-th/0005139].
7. H.A. Chamblin and H.S. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225]; N. Kaloper, Bent domain walls as braneworlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210]; A. Lukas, B.A. Ovrut and D. Waldram, Boundary inflation, Phys. Rev. D 61 (2000) 023506 [hep-th/9902071]; T. Nihei, Inflation in the five-dimensional universe with an orbifold extra dimension, Phys. Lett. B 465 (1999) 81 [hep-ph/9905487]; H.B. Kim and H.D. Kim, Inflation and gauge hierarchy in Randall-Sundrum compactification, Phys. Rev. D 61 (2000) 064003 [hep-th/9909053]; D.J. H. Chung and K. Freese, Cosmological challenges in theories with extra dimensions and remarks on the horizon problem, Phys. Rev. D 61 (2000) 023511 [hep-ph/9906542]; J. Garriga and M. Sasaki, Brane-world creation and black holes, Phys. Rev. D 62 (2000) 043523 [hep-th/9912118]; J.E. Kim and B. Kyae, Exact cosmological solution and modulus stabilization in the Randall-Sundrum model with bulk matter, Phys. Lett. B 486 (2000) 165 [hep-th/0005139].
8. H.A. Chamblin and H.S. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225]; N. Kaloper, Bent domain walls as braneworlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210]; A. Lukas, B.A. Ovrut and D. Waldram, Boundary inflation, Phys. Rev. D 61 (2000) 023506 [hep-th/9902071]; T. Nihei, Inflation in the five-dimensional universe with an orbifold extra dimension, Phys. Lett. B 465 (1999) 81 [hep-ph/9905487]; H.B. Kim and H.D. Kim, Inflation and gauge hierarchy in Randall-Sundrum compactification, Phys. Rev. D 61 (2000) 064003 [hep-th/9909053]; D.J. H. Chung and K. Freese, Cosmological challenges in theories with extra dimensions and remarks on the horizon problem, Phys. Rev. D 61 (2000) 023511 [hep-ph/9906542]; J. Garriga and M. Sasaki, Brane-world creation and black holes, Phys. Rev. D 62 (2000) 043523 [hep-th/9912118]; J.E. Kim and B. Kyae, Exact cosmological solution and modulus stabilization in the Randall-Sundrum model with bulk matter, Phys. Lett. B 486 (2000) 165 [hep-th/0005139].
9. H.A. Chamblin and H.S. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225]; N. Kaloper, Bent domain walls as braneworlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210]; A. Lukas, B.A. Ovrut and D. Waldram, Boundary inflation, Phys. Rev. D 61 (2000) 023506 [hep-th/9902071]; T. Nihei, Inflation in the five-dimensional universe with an orbifold extra dimension, Phys. Lett. B 465 (1999) 81 [hep-ph/9905487]; H.B. Kim and H.D. Kim, Inflation and gauge hierarchy in Randall-Sundrum compactification, Phys. Rev. D 61 (2000) 064003 [hep-th/9909053]; D.J. H. Chung and K. Freese, Cosmological challenges in theories with extra dimensions and remarks on the horizon problem, Phys. Rev. D 61 (2000) 023511 [hep-ph/9906542]; J. Garriga and M. Sasaki, Brane-world creation and black holes, Phys. Rev. D 62 (2000) 043523 [hep-th/9912118]; J.E. Kim and B. Kyae, Exact cosmological solution and modulus stabilization in the Randall-Sundrum model with bulk matter, Phys. Lett. B 486 (2000) 165 [hep-th/0005139].
10. H.A. Chamblin and H.S. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225]; N. Kaloper, Bent domain walls as braneworlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210]; A. Lukas, B.A. Ovrut and D. Waldram, Boundary inflation, Phys. Rev. D 61 (2000) 023506 [hep-th/9902071]; T. Nihei, Inflation in the five-dimensional universe with an orbifold extra dimension, Phys. Lett. B 465 (1999) 81 [hep-ph/9905487]; H.B. Kim and H.D. Kim, Inflation and gauge hierarchy in Randall-Sundrum compactification, Phys. Rev. D 61 (2000) 064003 [hep-th/9909053]; D.J. H. Chung and K. Freese, Cosmological challenges in theories with extra dimensions and remarks on the horizon problem, Phys. Rev. D 61 (2000) 023511 [hep-ph/9906542]; J. Garriga and M. Sasaki, Brane-world creation and black holes, Phys. Rev. D 62 (2000) 043523 [hep-th/9912118]; J.E. Kim and B. Kyae, Exact cosmological solution and modulus stabilization in the Randall-Sundrum model with bulk matter, Phys. Lett. B 486 (2000) 165 [hep-th/0005139].
11. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
12. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
13. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
14. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
15. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
16. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
17. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
18. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012]; J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523]; W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447]; S. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, J. High Energy Phys. 03 (2000) 023 [hep-th/0002091]; E.E. Flanagan, S.H. H. Tye and I. Wasserman, A cosmology of the brane world, Phys. Rev. D 62 (2000) 024011 [hep-ph/9909373]; C. Csáki, M. Graesser, C. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513]; P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481]; S. Mukohyama, T. Shiromizu and K. ichi Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287]; D. Youm, Bulk fields in dilatonic and self-tuning flat domain walls, hep-th/0002147; J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, hep-th/0003067; S.P. de Alwis, A.T. Flournoy and N. Irges, Brane worlds, the cosmological constant and string theory, hep-th/0004125; S. Nojiri, O. Obregon and S.D. Odintsov, (Non)-singular brane-world cosmology induced by quantum effects in D5 dilatonic gravity, hep-th/0005127; C.-J. Zhu, A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system, J. High Energy Phys. 06 (2000) 034 [hep-th/0005230]; Z. Kakushadze, Localized (super)gravity and cosmological constant, hep-th/0005217.
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