×

Eternal inflation in light of Wheeler-DeWitt equation. (English) Zbl 1486.83155

Summary: The Wheeler-DeWitt equation provides the probability distribution for the curvature perturbation, the gauge invariant quantum fluctuation of the inflaton. From this, we can find a tower of power spectra which is not found in a perturbative approach. Since the power spectrum for the modes that cross the horizon contributes to the uncertainty in the classical inflaton displacement, we obtain new conditions for eternal inflation. In the presence of the patch in the higher excitations, the bound on the slow-roll parameter allowing eternal inflation is given by at most \(\epsilon \lesssim (2n+1)(H/m_{\mathrm{Pl}})^2\) with \(n\) integer indicating the quantum number labelling the excitation. For large \(n\), the bound on \(\epsilon\) is relaxed such that eternal inflation can take place with even larger value of \(\epsilon\). While the second law of thermodynamics implies that \(n=0\) state is preferred, we cannot ignore such large \(n\) effect since the nonlinear interaction inducing transitions to the \(n=0\) state is suppressed.

MSC:

83E05 Geometrodynamics and the holographic principle
58J45 Hyperbolic equations on manifolds
83C45 Quantization of the gravitational field
83E30 String and superstring theories in gravitational theory
83F05 Relativistic cosmology
35B20 Perturbations in context of PDEs
68T37 Reasoning under uncertainty in the context of artificial intelligence
80A10 Classical and relativistic thermodynamics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] V.F. Mukhanov and G.V. Chibisov, 1981 Quantum fluctuations and a nonsingular universe JETP Lett.33 532
[2] V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, 1992 Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, https://doi.org/10.1016/0370-1573(92)90044-Z Phys. Rept.215 203 · doi:10.1016/0370-1573(92)90044-Z
[3] A.H. Guth, 1987 The inflationary universe: a possible solution to the horizon and flatness problems, https://doi.org/10.1103/PhysRevD.23.347 Adv. Ser. Astrophys. Cosmol.3 139 · Zbl 1371.83202 · doi:10.1103/PhysRevD.23.347
[4] A.D. Linde, 1987 A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, https://doi.org/10.1016/0370-2693(82)91219-9 Adv. Ser. Astrophys. Cosmol.3 149 · doi:10.1016/0370-2693(82)91219-9
[5] A. Albrecht and P.J. Steinhardt, 1987 Cosmology for grand unified theories with radiatively induced symmetry breaking, https://doi.org/10.1103/PhysRevLett.48.1220 Adv. Ser. Astrophys. Cosmol.3 158 · doi:10.1103/PhysRevLett.48.1220
[6] P.J. Steinhardt, 1982 Natural inflation, in The Very Early Universe, Proceedings of the Nuffield Workshop, Cambridge, 21 June-9 July, 1982, G.W. Gibbons, S.W. Hawking and S.T.C. Siklos eds., Cambridge University Press
[7] A. Vilenkin, 1983 The birth of inflationary universes, Phys. Rev. D27 2848 · doi:10.1103/PhysRevD.27.2848
[8] A.D. Linde, 1986 Eternal chaotic inflation, https://doi.org/10.1142/S0217732386000129 Mod. Phys. Lett. A1 81 · doi:10.1142/S0217732386000129
[9] A.D. Linde, 1986 Eternally existing selfreproducing chaotic inflationary universe, https://doi.org/10.1016/0370-2693(86)90611-8 Phys. Lett. B175 395 · doi:10.1016/0370-2693(86)90611-8
[10] A.S. Goncharov, A.D. Linde and V.F. Mukhanov, 1987 The global structure of the inflationary universe, https://doi.org/10.1142/S0217751X87000211 Int. J. Mod. Phys. A2 561 · Zbl 1165.83359 · doi:10.1142/S0217751X87000211
[11] A.H. Guth, 2007 Eternal inflation and its implications, https://doi.org/10.1088/1751-8113/40/25/S25 J. Phys. A40 6811 [hep-th/0702178] · doi:10.1088/1751-8113/40/25/S25
[12] G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, [1806.08362]
[13] H. Matsui and F. Takahashi, 2019 Eternal inflation and swampland conjectures, https://doi.org/10.1103/PhysRevD.99.023533 Phys. Rev. D99 023533 [1807.11938] · doi:10.1103/PhysRevD.99.023533
[14] K. Dimopoulos, 2018 Steep eternal inflation and the swampland, https://doi.org/10.1103/PhysRevD.98.123516 Phys. Rev. D98 123516 [1810.03438] · doi:10.1103/PhysRevD.98.123516
[15] H. Ooguri, E. Palti, G. Shiu and C. Vafa, 2019 Distance and de Sitter conjectures on the swampland, https://doi.org/10.1016/j.physletb.2018.11.018 Phys. Lett. B788 180 [1810.05506] · doi:10.1016/j.physletb.2018.11.018
[16] M.-S. Seo, 2019 de Sitter swampland bound in the Dirac-Born-Infeld inflation model, https://doi.org/10.1103/PhysRevD.99.106004 Phys. Rev. D99 106004 [1812.07670] · doi:10.1103/PhysRevD.99.106004
[17] M.-S. Seo, 2019 Thermodynamic interpretation of the de Sitter swampland conjecture, https://doi.org/10.1016/j.physletb.2019.134904 Phys. Lett. B797 134904 [1907.12142] · doi:10.1016/j.physletb.2019.134904
[18] H. Matsui and T. Terada, Swampland constraints on no-boundary quantum cosmology, [2006.03443] · Zbl 1456.83121
[19] M.-S. Seo, 2020 The entropic quasi-de Sitter instability time from the distance conjecture, https://doi.org/10.1016/j.physletb.2020.135580 Phys. Lett. B807 135580 [1911.06441] · Zbl 1473.83014 · doi:10.1016/j.physletb.2020.135580
[20] R.-G. Cai and S.-J. Wang, A refined trans-Planckian censorship conjecture, [1912.00607]
[21] S.K. Garg and C. Krishnan, 2019 Bounds on slow roll and the de Sitter Swampland J. High Energy Phys. JHEP11(2019)075 [1807.05193] · doi:10.1007/JHEP11(2019)075
[22] D. Andriot and C. Roupec, 2019 Further refining the de Sitter swampland conjecture, https://doi.org/10.1002/prop.201800105 Fortsch. Phys.67 1800105 [1811.08889] · Zbl 07762678 · doi:10.1002/prop.201800105
[23] W.H. Kinney, 2019 Eternal inflation and the refined swampland conjecture, https://doi.org/10.1103/PhysRevLett.122.081302 Phys. Rev. Lett.122 081302 [1811.11698] · doi:10.1103/PhysRevLett.122.081302
[24] T. Rudelius, 2019 Conditions for (no) eternal inflation J. Cosmol. Astropart. Phys.2019 08 009 [1905.05198] · Zbl 07468499
[25] T. Markkanen, 2016 Decoherence can relax cosmic acceleration J. Cosmol. Astropart. Phys.2016 11 026 [1609.01738]
[26] T. Markkanen, 2017 Decoherence can relax cosmic acceleration: an example J. Cosmol. Astropart. Phys.2017 09 022 [1610.06637] · Zbl 1515.83400
[27] C. Cheung, P. Creminelli, A. Fitzpatrick, J. Kaplan and L. Senatore, 2008 The effective field theory of inflation J. High Energy Phys. JHEP03(2008)014 [0709.0293]
[28] S. Weinberg, 2008 Effective field theory for inflation, https://doi.org/10.1103/PhysRevD.77.123541 Phys. Rev. D77 123541 [0804.4291] · doi:10.1103/PhysRevD.77.123541
[29] T. Prokopec and G. Rigopoulos, 2010 Path integral for inflationary perturbations, https://doi.org/10.1103/PhysRevD.82.023529 Phys. Rev. D82 023529 [1004.0882] · doi:10.1103/PhysRevD.82.023529
[30] J.-O. Gong, M.-S. Seo and G. Shiu, 2016 Path integral for multi-field inflation J. High Energy Phys. JHEP07(2016)099 [1603.03689] · Zbl 1390.83451 · doi:10.1007/JHEP07(2016)099
[31] A.H. Guth and S.-Y. Pi, 1985 The quantum mechanics of the scalar field in the new inflationary universe, https://doi.org/10.1103/PhysRevD.32.1899 Phys. Rev. D32 1899 · doi:10.1103/PhysRevD.32.1899
[32] A. Albrecht, P. Ferreira, M. Joyce and T. Prokopec, 1994 Inflation and squeezed quantum states, https://doi.org/10.1103/PhysRevD.50.4807 Phys. Rev. D50 4807 [astro-ph/9303001] · doi:10.1103/PhysRevD.50.4807
[33] A.A. Starobinsky, 1986 Stochastic de Sitter (inflationary) stage in the early universe, https://doi.org/10.1007/3-540-16452-9_6 Lect. Notes Phys.246 107 · doi:10.1007/3-540-16452-9_6
[34] C. Kiefer, 2012 Quantum gravity, 3rd ed., Int. Ser. Monogr. Phys.155 , Oxford University Press · Zbl 1243.83002
[35] R.L. Arnowitt, S. Deser and C.W. Misner, 2008 The Dynamics of general relativity, https://doi.org/10.1007/s10714-008-0661-1 Gen. Rel. Grav.40 1997 [gr-qc/0405109] · Zbl 1152.83320 · doi:10.1007/s10714-008-0661-1
[36] J.A. Wheeler, 1964 Relativity, groups and topology Les Houches Lectures, 1963, C. DeWitt and B. DeWitt eds., New York: Gordon and Breach · Zbl 0125.27406
[37] B.S. DeWitt, 1967 Quantum theory of gravity. 1. The canonical theory, https://doi.org/10.1103/PhysRev.160.1113 Phys. Rev.1601113 · Zbl 0158.46504 · doi:10.1103/PhysRev.160.1113
[38] T. Banks, 1985 T C P, quantum gravity, the cosmological constant and all that..., https://doi.org/10.1016/0550-3213(85)90020-3 Nucl. Phys. B249 332 · doi:10.1016/0550-3213(85)90020-3
[39] R. Brout, G. Horwitz and D. Weil, 1987 On the onset of time and temperature in cosmology, https://doi.org/10.1016/0370-2693(87)90114-6 Phys. Lett. B192 318 · doi:10.1016/0370-2693(87)90114-6
[40] R. Brout, 1987 On the concept of time and the origin of the cosmological temperature, https://doi.org/10.1007/BF01882790 Found. Phys.17 603 · doi:10.1007/BF01882790
[41] R. Brout and G. Venturi, 1989 Time in semiclassical gravity, https://doi.org/10.1103/PhysRevD.39.2436 Phys. Rev. D39 2436 · doi:10.1103/PhysRevD.39.2436
[42] J.J. Halliwell and S.W. Hawking, 1987 The origin of structure in the universe, https://doi.org/10.1103/PhysRevD.31.1777 Adv. Ser. Astrophys. Cosmol.3 277 · doi:10.1103/PhysRevD.31.1777
[43] A.Y. Kamenshchik, A. Tronconi and G. Venturi, 2013 Inflation and quantum gravity in a Born-Oppenheimer context, https://doi.org/10.1016/j.physletb.2013.08.067 Phys. Lett. B726 518 [1305.6138] · Zbl 1311.83019 · doi:10.1016/j.physletb.2013.08.067
[44] A.Y. Kamenshchik, A. Tronconi and G. Venturi, 2014 Signatures of quantum gravity in a Born-Oppenheimer context, https://doi.org/10.1016/j.physletb.2014.05.028 Phys. Lett. B734 72 [1403.2961] · Zbl 1380.81468 · doi:10.1016/j.physletb.2014.05.028
[45] A.Y. Kamenshchik, A. Tronconi and G. Venturi, 2016 Quantum cosmology and the evolution of inflationary spectra, https://doi.org/10.1103/PhysRevD.94.123524 Phys. Rev. D94 123524 [1609.02830] · doi:10.1103/PhysRevD.94.123524
[46] A.E. Faraggi and M. Matone, The geometrical origin of dark energy, [2006.11935]
[47] C. Kiefer and M. Kraemer, 2012 Quantum gravitational contributions to the CMB anisotropy spectrum, https://doi.org/10.1103/PhysRevLett.108.021301 Phys. Rev. Lett.108 021301 [1103.4967] · doi:10.1103/PhysRevLett.108.021301
[48] C. Kiefer and T.P. Singh, 1991 Quantum gravitational corrections to the functional Schrödinger equation, https://doi.org/10.1103/PhysRevD.44.1067 Phys. Rev. D44 1067 · doi:10.1103/PhysRevD.44.1067
[49] C. Bertoni, F. Finelli and G. Venturi, 1996 The Born-Oppenheimer approach to the matter - gravity system and unitarity, https://doi.org/10.1088/0264-9381/13/9/005 Class. Quant. Grav.13 2375 [gr-qc/9604011] · Zbl 0855.58065 · doi:10.1088/0264-9381/13/9/005
[50] A.Y. Kamenshchik, A. Tronconi and G. Venturi, 2018 The Born-Oppenheimer method, quantum gravity and matter, https://doi.org/10.1088/1361-6382/aa8fb3 Class. Quant. Grav.35 015012 [1709.10361] · Zbl 1382.83136 · doi:10.1088/1361-6382/aa8fb3
[51] D. Brizuela, C. Kiefer, M. Kraemer and S. Robles-Pérez, 2019 Quantum-gravity effects for excited states of inflationary perturbations, https://doi.org/10.1103/PhysRevD.99.104007 Phys. Rev. D99 104007 [1903.01234] · doi:10.1103/PhysRevD.99.104007
[52] R. Bousso, B. Freivogel and I.-S. Yang, 2006 Eternal inflation: the inside story, https://doi.org/10.1103/PhysRevD.74.103516 Phys. Rev. D74 103516 [hep-th/0606114] · doi:10.1103/PhysRevD.74.103516
[53] N. Arkani-Hamed, S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, 2007 A measure of de Sitter entropy and eternal inflation J. High Energy Phys. JHEP05(2007)055 [0704.1814]
[54] Z. Wang, R. Brandenberger and L. Heisenberg, 2020 Eternal inflation, entropy bounds and the swampland, https://doi.org/10.1140/epjc/s10052-020-8412-x Eur. Phys. J. C80 864 [1907.08943] · doi:10.1140/epjc/s10052-020-8412-x
[55] V.F. Mukhanov, 1985 Gravitational instability of the universe filled with a scalar field JETP Lett.41 493
[56] M. Sasaki, 1986 Large scale quantum fluctuations in the inflationary universe, https://doi.org/10.1143/PTP.76.1036 Prog. Theor. Phys.76 1036 · doi:10.1143/PTP.76.1036
[57] J.-Y. Ji, J.K. Kim, S.P. Kim and K.-S. Soh, 1995 Exact wave functions and nonadiabatic Berry phases of a time-dependent harmonic oscillator, https://doi.org/10.1103/PhysRevA.52.3352 Phys. Rev. A52 3352 · doi:10.1103/PhysRevA.52.3352
[58] I.A. Pedrosa, 1997 Exact wave functions of a harmonic oscillator with time-dependent mass and frequency, https://doi.org/10.1103/PhysRevA.55.3219 Phys. Rev. A55 3219 · doi:10.1103/PhysRevA.55.3219
[59] H.R. Lewis and W.B. Riesenfeld, 1969 An Exact quantum theory of the time dependent harmonic oscillator and of a charged particle time dependent electromagnetic field, https://doi.org/10.1063/1.1664991 J. Math. Phys.10 1458 · Zbl 1317.81109 · doi:10.1063/1.1664991
[60] A. Vilenkin and L.H. Ford, 1982 Gravitational effects upon cosmological phase transitions, https://doi.org/10.1103/PhysRevD.26.1231 Phys. Rev. D26 1231 · doi:10.1103/PhysRevD.26.1231
[61] A.D. Linde, 1982 Scalar field fluctuations in expanding universe and the new inflationary universe scenario, https://doi.org/10.1016/0370-2693(82)90293-3 Phys. Lett. B116 335 · doi:10.1016/0370-2693(82)90293-3
[62] A.A. Starobinsky, 1982 Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations, https://doi.org/10.1016/0370-2693(82)90541-X Phys. Lett. B117 175 · doi:10.1016/0370-2693(82)90541-X
[63] F. Reif, 1965 Fundamentals of statistical and thermal physics, McGraw-Hill, New York
[64] J.M. Maldacena, 2003 Non-Gaussian features of primordial fluctuations in single field inflationary models J. High Energy Phys. JHEP05(2003)013 [astro-ph/0210603]
[65] E. Nelson, 2016 Quantum decoherence during inflation from gravitational nonlinearities J. Cosmol. Astropart. Phys.2016 03 022 [1601.03734]
[66] J.-O. Gong and M.-S. Seo, 2019 Quantum non-linear evolution of inflationary tensor perturbations J. High Energy Phys. JHEP05(2019)021 [1903.12295] · Zbl 1416.83153 · doi:10.1007/JHEP05(2019)021
[67] A. Bedroya and C. Vafa, 2020 Trans-Planckian censorship and the swampland J. High Energy Phys. JHEP09(2020)123 [1909.11063] · Zbl 1454.85006 · doi:10.1007/JHEP09(2020)123
[68] P. Hayden and J. Preskill, 2007 Black holes as mirrors: quantum information in random subsystems J. High Energy Phys. JHEP09(2007)120 [0708.4025]
[69] Y. Sekino and L. Susskind, 2008 Fast Scramblers J. High Energy Phys. JHEP10(2008)065 [0808.2096]
[70] J.-O. Gong and M.-S. Seo, 2020 Quantum nature of Wigner function for inflationary tensor perturbations J. High Energy Phys. JHEP03(2020)060 [2002.01064] · Zbl 1435.83211 · doi:10.1007/JHEP03(2020)060
[71] K.K. Boddy, S.M. Carroll and J. Pollack, 2017 How decoherence affects the probability of slow-roll eternal inflation, https://doi.org/10.1103/PhysRevD.96.023539 Phys. Rev. D96 023539 [1612.04894] · doi:10.1103/PhysRevD.96.023539
[72] G.W. Gibbons and S.W. Hawking, 1977 Cosmological event horizons, thermodynamics, and particle creation, https://doi.org/10.1103/PhysRevD.15.2738 Phys. Rev. D15 2738 · doi:10.1103/PhysRevD.15.2738
[73] H. Ooguri and C. Vafa, 2007 On the geometry of the string landscape and the swampland, https://doi.org/10.1016/j.nuclphysb.2006.10.033 Nucl. Phys. B766 21 [hep-th/0605264] · Zbl 1117.81117 · doi:10.1016/j.nuclphysb.2006.10.033
[74] R. Bousso, 1999 A Covariant entropy conjecture J. High Energy Phys. JHEP07(1999)004 [hep-th/9905177] · Zbl 0951.83011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.