Abstract
We study Fubini instantons of a self-gravitating scalar field. The Fubini instanton describes the decay of a vacuum state under tunneling instead of rolling in the presence of a tachyonic potential. The tunneling occurs from the maximum of the potential, which is a vacuum state, to any arbitrary state, belonging to the tunneling without any barrier. We consider two different types of the tachyonic potential. One has only a quartic term. The other has both the quartic and quadratic terms. We show that, there exist several kinds of new O(4)-symmetric Fubini instanton solution, which are possible only if gravity is taken into account. One type of them has the structure with Z 2 symmetry. This type of the solution is possible only in the de Sitter background. We discuss on the interpretation of the solutions with Z 2 symmetry.
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References
A.D. Linde, Nonsingular regenerating inflationary universe, Cambridge University preprint, Print-82-0554.
A. Vilenkin, The Birth of Inflationary Universes, Phys. Rev. D 27 (1983) 2848.
A. Vilenkin, Eternal inflation and chaotic terminology, gr-qc/0409055 [INSPIRE].
A.D. Linde, Eternally Existing Selfreproducing Chaotic Inflationary Universe, Phys. Lett. B 175 (1986) 395 [INSPIRE].
A.H. Guth, Inflation and eternal inflation, Phys. Rep. 333–334 (2000) 555.
S. Winitzki, Predictions in eternal inflation, Lect. Notes Phys. 738 (2008) 157 [gr-qc/0612164] [INSPIRE]
R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].
L. Susskind, The Anthropic landscape of string theory, hep-th/0302219 [INSPIRE].
J. Garriga and A. Vilenkin, Recycling universe, Phys. Rev. D 57 (1998) 2230 [astro-ph/9707292] [INSPIRE].
A. Borde, A.H. Guth and A. Vilenkin, Inflationary space-times are incompletein past directions, Phys. Rev. Lett. 90 (2003) 151301 [gr-qc/0110012] [INSPIRE].
A. Mithani and A. Vilenkin, Did the universe have a beginning?, arXiv:1204.4658 [INSPIRE].
L. Susskind, Was There a Beginning?, arXiv:1204.5385 [INSPIRE].
L. Susskind, Is Eternal Inflation Past-Eternal? And What if It Is?, arXiv:1205.0589 [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. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [INSPIRE].
C. Hull, The minimal couplings and scalar potentials of the gauged N = 8 supergravities, Class. Quant. Grav. 2 (1985) 343 [INSPIRE].
R. Kallosh, A.D. Linde, S. Prokushkin and M. Shmakova, Gauged supergravities, de Sitter space and cosmology, Phys. Rev. D 65 (2002) 105016 [hep-th/0110089] [INSPIRE].
R. Kallosh, A.D. Linde, S. Prokushkin and M. Shmakova, Supergravity, dark energy and the fate of the universe, Phys. Rev. D 66 (2002) 123503 [hep-th/0208156] [INSPIRE].
R. Kallosh and A.D. Linde, M theory, cosmological constant and anthropic principle, Phys. Rev. D 67 (2003) 023510 [hep-th/0208157] [INSPIRE].
H. Kim, Supergravity approach to tachyon potential in brane - anti-brane systems, JHEP 01 (2003) 080 [hep-th/0204191] [INSPIRE].
A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Yu.S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. 59B (1975) 85.
S. Coleman, Aspects of symmetry, Cambridge University Press, Cambridge England U.K. (1985).
I. Herbut, A Modern Approach to Critical Phenomena, Cambridge University Press, Cambridge, Cambridge U.K. (2007).
I.Y. Kobzarev, L. Okun and M. Voloshin, Bubbles in Metastable Vacuum, Sov. J. Nucl. Phys. 20 (1975)644 [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 16 (1977) 1248] [INSPIRE].
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
S. Parke, Gravity and the decay of the false vacuum, Phys. Lett. 121B (1983) 313.
K.-M. Lee and E.J. Weinberg, Decay of the true vacuum in curved space-time, Phys. Rev. D 36 (1987) 1088 [INSPIRE].
B.-H. Lee and W. Lee, Vacuum bubbles in a de Sitter background and black hole pair creation, Class. Quant. Grav. 26 (2009) 225002 [arXiv:0809.4907] [INSPIRE].
S. Fubini, A New Approach to Conformal Invariant Field Theories, Nuovo Cim. A 34 (1976) 521 [INSPIRE].
A.D. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Phys. B 216 (1983) 421 [Erratum ibid. B 223 (1983) 544] [INSPIRE].
K.-M. Lee and E.J. Weinberg, Tunneling without barriers, Nucl. Phys. B 267 (1986) 181 [INSPIRE].
K.-M. Lee, Tunneling without barriers in curved space-time, Nucl. Phys. B 282 (1987) 509 [INSPIRE].
L.G. Jensen and P.J. Steinhardt, Bubble nucleation for flat potential barriers, Nucl. Phys. B 317 (1989) 693 [INSPIRE].
B.-H. Lee, C.H. Lee, W. Lee and C. Oh, Oscillating instanton solutions in curved space, Phys. Rev. D 85 (2012) 024022 [arXiv:1106.5865] [INSPIRE].
S. Kanno, M. Sasaki and J. Soda, Tunneling without barriers with gravity, Class. Quant. Grav. 29 (2012) 075010 [arXiv:1201.2272] [INSPIRE].
S. Kanno, M. Sasaki and J. Soda, Destabilizing Tachyonic Vacua at or above the BF Bound, Prog. Theor. Phys. 128 (2012) 213 [arXiv:1203.0612] [INSPIRE].
J. Garriga, X. Montes, M. Sasaki and T. Tanaka, Spectrum of cosmological perturbations in the one bubble open universe, Nucl. Phys. B 551 (1999) 317 [astro-ph/9811257] [INSPIRE].
S. Khlebnikov, Decoherence, instantons and cosmological horizons, Nucl. Phys. B 631 (2002) 307 [hep-ph/0111194] [INSPIRE].
F. Loran, Fubini vacua as a classical de Sitter vacua, Mod. Phys. Lett. A 22 (2007) 2217 [hep-th/0612089] [INSPIRE].
S. de Haro and A.C. Petkou, Instantons and Conformal Holography, JHEP 12 (2006) 076 [hep-th/0606276] [INSPIRE].
S. de Haro, I. Papadimitriou and A.C. Petkou, Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS 4, Phys. Rev. Lett. 98 (2007) 231601 [hep-th/0611315] [INSPIRE].
J.L. Barbon and E. Rabinovici, Holography of AdS vacuum bubbles, JHEP 04 (2010) 123 [arXiv:1003.4966] [INSPIRE].
J. Barbon and E. Rabinovici, AdS Crunches, CFT Falls And Cosmological Complementarity, JHEP 04 (2011) 044 [arXiv:1102.3015] [INSPIRE].
A. Kuznetsov and P. Tinyakov, Numerical study of induced false vacuum decay at high-energies, Mod. Phys. Lett. A 11 (1996) 479 [hep-ph/9510310] [INSPIRE].
A. Kuznetsov and P. Tinyakov, False vacuum decay induced by particle collisions, Phys. Rev. D 56 (1997) 1156 [hep-ph/9703256] [INSPIRE].
A. Yurova and A. Yurov, Generalized Fubini instantons, Phys. Lett. A 372 (2008) 4222 [arXiv:0709.2546] [INSPIRE].
C.M. Bender and T. Wu, Anharmonic oscillator. 2: A Study of perturbation theory in large order, Phys. Rev. D 7 (1973) 1620 [INSPIRE].
J.-Q. Liang and H. Muller-Kirsten, Bounces and the calculation of quantum tunneling effects, Phys. Rev. D 45 (1992) 2963 [Erratum ibid. D 48 (1993) 964] [INSPIRE].
L.N. Lipatov, Divergence of the Perturbation Theory Series and the Quasiclassical Theory, Sov. Phys. JETP 45 (1977) 216.
I. Affleck, On Constrained Instantons, Nucl. Phys. B 191 (1981) 429 [INSPIRE].
J.W. York Jr., Role of Conformal Three-Geometry in the Dynamics of Gravitation, Phys. Rev. Lett. 28 (1972) 1082.
G. Gibbons and S. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J.W. York Jr., Boundary Terms in the Action Principles of General Relativity, Found. Phys. 16 (1986)249.
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, Freeman, San Francisco (1973).
B.K. Berger, Why solve the Hamiltonian constraint in numerical relativity?, Gen. Rel. Grav. 38 (2006) 625 [gr-qc/0410058] [INSPIRE].
W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in Fortran, Cambridge University Press, Cambridge England U.K. (1992).
C.G. Callan Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].
E.J. Weinberg, Vacuum decay in theories with symmetry breaking by radiative corrections, Phys. Rev. D 47 (1993) 4614 [hep-ph/9211314] [INSPIRE].
J. Baacke and G. Lavrelashvili, One loop corrections to the metastable vacuum decay, Phys. Rev. D 69 (2004) 025009 [hep-th/0307202] [INSPIRE].
G.V. Dunne and H. Min, Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay, Phys. Rev. D 72 (2005) 125004 [hep-th/0511156] [INSPIRE].
B.-H. Lee, W. Lee, D. Ro and D.-h. Yeom, in progress.
G. Gibbons, S. Hawking and M. Perry, Path Integrals and the Indefiniteness of the Gravitational Action, Nucl. Phys. B 138 (1978) 141 [INSPIRE].
A. Dasgupta and R. Loll, A Proper time cure for the conformal sickness in quantum gravity, Nucl. Phys. B 606 (2001) 357 [hep-th/0103186] [INSPIRE].
J.C. Hackworth and E.J. Weinberg, Oscillating bounce solutions and vacuum tunneling in de Sitter spacetime, Phys. Rev. D 71 (2005) 044014 [hep-th/0410142] [INSPIRE].
E.J. Weinberg, New bounce solutions and vacuum tunneling in de Sitter spacetime, AIP Conf. Proc. 805 (2006) 259 [hep-th/0512332] [INSPIRE].
G. Lavrelashvili, The Number of negative modes of the oscillating bounces, Phys. Rev. D 73 (2006) 083513 [gr-qc/0602039] [INSPIRE].
G.V. Dunne and Q.-h. Wang, Fluctuations about Cosmological Instantons, Phys. Rev. D 74 (2006) 024018 [hep-th/0605176] [INSPIRE].
A.R. Brown and E.J. Weinberg, Thermal derivation of the Coleman-De Luccia tunneling prescription, Phys. Rev. D 76 (2007) 064003 [arXiv:0706.1573] [INSPIRE].
A. Vilenkin, Topological inflation, Phys. Rev. Lett. 72 (1994) 3137 [hep-th/9402085] [INSPIRE].
A.D. Linde, Monopoles as big as a universe, Phys. Lett. B 327 (1994) 208 [astro-ph/9402031] [INSPIRE].
J.B. Hartle, S. Hawking and T. Hertog, No-Boundary Measure of the Universe, Phys. Rev. Lett. 100 (2008) 201301 [arXiv:0711.4630] [INSPIRE].
J.B. Hartle, S. Hawking and T. Hertog, The Classical Universes of the No-Boundary Quantum State, Phys. Rev. D 77 (2008) 123537 [arXiv:0803.1663] [INSPIRE].
D.-i. Hwang, H. Sahlmann and D.-h. Yeom, The no-boundary measure in scalartensor gravity, Class. Quant. Grav. 29 (2012) 095005 [arXiv:1107.4653] [INSPIRE].
D.-i. Hwang, B.-H. Lee, H. Sahlmann and D.-h. Yeom, The no-boundary measure in string theory: applications to moduli stabilization, flux compactification and cosmic landscape, Class. Quant. Grav. 29 (2012) 175001. [arXiv:1203.0112] [INSPIRE].
A. Vilenkin, Quantum origin of the universe, Nucl. Phys. B 252 (1985) 141 [INSPIRE].
R. Bousso and A.D. Linde, Quantum creation of a universe with omega does not = 1: Singular and nonsingular instantons, Phys. Rev. D 58 (1998) 083503 [gr-qc/9803068] [INSPIRE].
J. Garriga and A. Megevand, Coincident brane nucleation and the neutralization of Lambda, Phys. Rev. D 69 (2004) 083510 [hep-th/0310211] [INSPIRE].
J. Garriga and A. Megevand, Decay of de Sitter vacua by thermal activation, Int. J. Theor. Phys. 43 (2004) 883 [hep-th/0404097] [INSPIRE].
A. Masoumi and E.J. Weinberg, Bounces with O(3) × O(2) symmetry, Phys. Rev. D 86 (2012) 104029 [arXiv:1207.3717] [INSPIRE].
S.R. Coleman, Quantum tunneling and negative eigenvalues, Nucl. Phys. B 298 (1988) 178 [INSPIRE].
T. Tanaka and M. Sasaki, False vacuum decay with gravity: Negative mode problem, Prog. Theor. Phys. 88 (1992) 503 [INSPIRE].
T. Tanaka, The No - negative mode theorem in false vacuum decay with gravity, Nucl. Phys. B 556 (1999) 373 [gr-qc/9901082] [INSPIRE].
A.R. Brown and A. Dahlen, The Case of the Disappearing Instanton, Phys. Rev. D 84 (2011) 105004 [arXiv:1106.0527] [INSPIRE].
G.V. Lavrelashvili, V.A. Rubakov and P.G. Tinyakov, Tunneling transitions with gravitation: breakdown of the quasiclassical approximation, Phys. Lett. 161B (1985) 280.
A. Khvedelidze, G.V. Lavrelashvili and T. Tanaka, On cosmological perturbations in closed FRW model with scalar field and false vacuum decay, Phys. Rev. D 62 (2000) 083501 [gr-qc/0001041] [INSPIRE].
G.V. Lavrelashvili, Negative mode problem in false vacuum decay with gravity, Nucl. Phys. Proc. Suppl. 88 (2000) 75 [gr-qc/0004025] [INSPIRE].
L. Battarra, G. Lavrelashvili and J.-L. Lehners, Negative Modes of Oscillating Instantons, Phys. Rev. D 86 (2012) 124001 [arXiv:1208.2182] [INSPIRE].
B.-H. Lee, W. Lee and D.-h. Yeom, Oscillating instantons as homogeneous tunneling channels, arXiv:1206.7040 [INSPIRE].
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Lee, BH., Lee, W., Oh, C. et al. Fubini instantons in curved space. J. High Energ. Phys. 2013, 3 (2013). https://doi.org/10.1007/JHEP06(2013)003
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DOI: https://doi.org/10.1007/JHEP06(2013)003