Advertisement

Cosmological daemon

  • I. Ya. Aref’eva
  • I. V. Volovich
Article

Abstract

Classical versions of the Big Bang cosmological models of the universe contain a singularity at the start of time, hence the time variable in the field equations should run over a half-line. Nonlocal string field theory equations with infinite number of derivatives are considered and an important difference between nonlocal operators on the whole real line and on a half-line is pointed out. We use the heat equation method and show that on the half-line in addition to the usual initial data a new arbitrary function (external source) occurs that we call the daemon function. The daemon function governs the evolution of the universe similar to Maxwell’s demon in thermodynamics. The universe and multiverse are open systems interacting with the daemon environment. In the simplest case the nonlocal scalar field reduces to the usual local scalar field coupled with an external source which is discussed in the stochastic approach to inflation. The daemon source can help to get the chaotic inflation scenario with a small scalar field.

Keywords

Cosmology of Theories beyond the SM D-branes String Field Theory 

References

  1. [1]
    A.D. Linde, Inflation and quantum cosmology, Academic Press, Boston U.S.A. (1990) [SPIRES].MATHGoogle Scholar
  2. [2]
    V. Mukhanov, Physical foundations of cosmology, Cambridge University Press, Cambridge U.K. (2005) [SPIRES].CrossRefMATHGoogle Scholar
  3. [3]
    S. Weinberg, Cosmology, Oxford University Press, Oxford U.K. (2008) [SPIRES].MATHGoogle Scholar
  4. [4]
    D.S. Gorbunov and V.A. Rubakov, Introduction to the theory of the early universe. Cosmological perturbations. Inflation (in Russian), Krasand, U.R.S.S. (2010).Google Scholar
  5. [5]
    S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge U.K. (1973) [SPIRES].CrossRefMATHGoogle Scholar
  6. [6]
    I.Y. Aref’eva, Nonlocal string tachyon as a model for cosmological dark energy, AIP Conf. Proc. 826 (2006) 301 [astro-ph/0410443] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  7. [7]
    I.Y. Aref’eva, A.S. Koshelev and S.Y. Vernov, Exactly solvable SFT inspired phantom model, Theor. Math. Phys. 148 (2006) 895 [astro-ph/0412619] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    I.Y. Aref’eva and L.V. Joukovskaya, Time lumps in nonlocal stringy models and cosmological applications, JHEP 10 (2005) 087 [hep-th/0504200] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    I.Y. Aref’eva, A.S. Koshelev and S.Y. Vernov, Stringy dark energy model with cold dark matter, Phys. Lett. B 628 (2005) 1 [astro-ph/0505605] [SPIRES].ADSGoogle Scholar
  10. [10]
    I.Y. Aref’eva, A.S. Koshelev and S.Y. Vernov, Crossing of the w = − 1 barrier by D3-brane dark energy model, Phys. Rev. D 72 (2005) 064017 [astro-ph/0507067] [SPIRES].ADSGoogle Scholar
  11. [11]
    G. Calcagni, Cosmological tachyon from cubic string field theory, JHEP 05 (2006) 012 [hep-th/0512259] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    I.Y. Aref’eva and A.S. Koshelev, Cosmic acceleration and crossing of w = − 1 barrier from cubic superstring field theory, JHEP 02 (2007) 041 [hep-th/0605085] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    I.Y. Aref’eva and I.V. Volovich, On the null energy condition and cosmology, Theor. Math. Phys. 155 (2008) 503 [hep-th/0612098] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  14. [14]
    N. Barnaby, T. Biswas and J.M. Cline, p-adic inflation, JHEP 04 (2007) 056 [hep-th/0612230] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    A.S. Koshelev, Non-local SFT tachyon and cosmology, JHEP 04 (2007) 029 [hep-th/0701103] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    I.Y. Aref’eva, L.V. Joukovskaya and S.Y. Vernov, Bouncing and accelerating solutions in nonlocal stringy models, JHEP 07 (2007) 087 [hep-th/0701184] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  17. [17]
    I.Y. Aref’eva and I.V. Volovich, Quantization of the Riemann zeta-function and cosmology, Int. J. Geom. Meth. Mod. Phys. 4 (2007) 881 [hep-th/0701284] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  18. [18]
    J.E. Lidsey, Stretching the inflaton potential with kinetic energy, Phys. Rev. D 76 (2007) 043511 [hep-th/0703007] [SPIRES].ADSGoogle Scholar
  19. [19]
    N. Barnaby and J.M. Cline, Large nongaussianity from nonlocal inflation, JCAP 07 (2007) 017 [arXiv:0704.3426] [SPIRES].ADSGoogle Scholar
  20. [20]
    G. Calcagni, M. Montobbio and G. Nardelli, Route to nonlocal cosmology, Phys. Rev. D 76 (2007) 126001 [arXiv:0705.3043] [SPIRES].ADSMathSciNetGoogle Scholar
  21. [21]
    L. Joukovskaya, Dynamics in nonlocal cosmological models derived from string field theory, Phys. Rev. D 76 (2007) 105007 [arXiv:0707.1545] [SPIRES].ADSMathSciNetGoogle Scholar
  22. [22]
    N. Barnaby and N. Kamran, Dynamics with infinitely many derivatives: the initial value problem, JHEP 02 (2008) 008 [arXiv:0709.3968] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  23. [23]
    L. Joukovskaya, Rolling tachyon in nonlocal cosmology, AIP Conf. Proc. 957 (2007) 325 [arXiv:0710.0404] [SPIRES].CrossRefADSGoogle Scholar
  24. [24]
    I.Y. Aref’eva, Stringy model of cosmological dark energy, AIP Conf. Proc. 957 (2007) 297 [arXiv:0710.3017] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  25. [25]
    I.Y. Aref’eva, L.V. Joukovskaya and S.Y. Vernov, Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric, J. Phys. A 41 (2008) 304003 [arXiv:0711.1364] [SPIRES].MathSciNetGoogle Scholar
  26. [26]
    G. Calcagni and G. Nardelli, Tachyon solutions in boundary and cubic string field theory, Phys. Rev. D 78 (2008) 126010 [arXiv:0708.0366] [SPIRES].ADSMathSciNetGoogle Scholar
  27. [27]
    G. Calcagni, M. Montobbio and G. Nardelli, Localization of nonlocal theories, Phys. Lett. B 662 (2008) 285 [arXiv:0712.2237] [SPIRES].ADSMathSciNetGoogle Scholar
  28. [28]
    N. Barnaby and J.M. Cline, Predictions for nongaussianity from nonlocal inflation, JCAP 06 (2008) 030 [arXiv:0802.3218] [SPIRES].ADSGoogle Scholar
  29. [29]
    J.E. Lidsey, Non-local inflation around a local maximum, Int. J. Mod. Phys. D 17 (2008) 577 [SPIRES].ADSMathSciNetGoogle Scholar
  30. [30]
    G. Calcagni and G. Nardelli, Nonlocal instantons and solitons in string models, Phys. Lett. B 669 (2008) 102 [arXiv:0802.4395] [SPIRES].ADSMathSciNetGoogle Scholar
  31. [31]
    I.Y. Aref’eva and A.S. Koshelev, Cosmological signature of tachyon condensation, JHEP 09 (2008) 068 [arXiv:0804.3570] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  32. [32]
    D.J. Mulryne and N.J. Nunes, Diffusing non-local inflation: solving the field equations as an initial value problem, Phys. Rev. D 78 (2008) 063519 [arXiv:0805.0449] [SPIRES].ADSMathSciNetGoogle Scholar
  33. [33]
    L. Joukovskaya, Dynamics with infinitely many time derivatives in Friedmann-Robertson-Walker background and rolling tachyon, JHEP 02 (2009) 045 [arXiv:0807.2065] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  34. [34]
    N. Barnaby and N. Kamran, Dynamics with infinitely many derivatives: variable coefficient equations, JHEP 12 (2008) 022 [arXiv:0809.4513] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  35. [35]
    N.J. Nunes and D.J. Mulryne, Non-linear non-local cosmology, AIP Conf. Proc. 1115 (2009) 329 [arXiv:0810.5471] [SPIRES].CrossRefADSGoogle Scholar
  36. [36]
    N. Barnaby, D.J. Mulryne, N.J. Nunes and P. Robinson, Dynamics and stability of light-like tachyon condensation, JHEP 03 (2009) 018 [arXiv:0811.0608] [SPIRES].CrossRefADSGoogle Scholar
  37. [37]
    N. Barnaby, Nonlocal inflation, Can. J. Phys. 87 (2009) 189 [arXiv:0811.0814] [SPIRES].CrossRefADSGoogle Scholar
  38. [38]
    A.S. Koshelev and S.Y. Vernov, Cosmological perturbations in SFT inspired non-local scalar field models, arXiv:0903.5176 [SPIRES].
  39. [39]
    G. Calcagni and G. Nardelli, Kinks of open superstring field theory, Nucl. Phys. B 823 (2009) 234 [arXiv:0904.3744] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  40. [40]
    G. Calcagni and G. Nardelli, Cosmological rolling solutions of nonlocal theories, Int. J. Mod. Phys. D 19 (2010) 329 [arXiv:0904.4245] [SPIRES].ADSMathSciNetGoogle Scholar
  41. [41]
    G. Calcagni and G. Nardelli, String theory as a diffusing system, JHEP 02 (2010) 093 [arXiv:0910.2160] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  42. [42]
    S.Y. Vernov, Localization of nonlocal cosmological models with quadratic potentials in the case of double roots, Class. Quant. Grav. 27 (2010) 035006 [arXiv:0907.0468] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  43. [43]
    G. Calcagni and G. Nardelli, Nonlocal gravity and the diffusion equation, Phys. Rev. D 82 (2010) 123518 [arXiv:1004.5144] [SPIRES].ADSGoogle Scholar
  44. [44]
    S.Y. Vernov, Localization of the SFT inspired nonlocal linear models and exact solutions, Phys. Part. Nucl. Lett. 8 (2011) 310 [arXiv:1005.0372] [SPIRES].CrossRefGoogle Scholar
  45. [45]
    S.Y. Vernov, Exact solutions for nonlocal nonlinear field equations in cosmology, Theor. Math. Phys. 166 (2011) 392 [arXiv:1005.5007] [SPIRES].CrossRefGoogle Scholar
  46. [46]
    A.S. Koshelev and S.Y. Vernov, Analysis of scalar perturbations in cosmological models with a non-local scalar field, Class. Quant. Grav. 28 (2011) 085019 [arXiv:1009.0746] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  47. [47]
    F. Galli and A.S. Koshelev, Multi-scalar field cosmology from SFT: an exactly solvable approximation, Theor. Math. Phys. 164 (2010) 1169 [Teor. Mat. Fiz. 164 (2010) 401] [arXiv:1010.1773] [SPIRES].CrossRefGoogle Scholar
  48. [48]
    F. Galli and A.S. Koshelev, Perturbative stability of SFT-based cosmological models, JCAP 05 (2011) 012 [arXiv:1011.5672] [SPIRES].ADSGoogle Scholar
  49. [49]
    I. Aref’eva, Puzzles with tachyon in SSFT and cosmological applications, Prog. Theor. Phys. Suppl. 188 (2011) 29 [arXiv:1101.5338] [SPIRES].CrossRefMATHADSGoogle Scholar
  50. [50]
    K. Ohmori, A review on tachyon condensation in open string field theories, hep-th/0102085 [SPIRES].
  51. [51]
    I.Y. Aref’eva, D.M. Belov, A.A. Giryavets, A.S. Koshelev and P.B. Medvedev, Noncommutative field theories and (super)string field theories, hep-th/0111208 [SPIRES].
  52. [52]
    W. Taylor and B. Zwiebach, D-branes, tachyons and string field theory, hep-th/0311017 [SPIRES].
  53. [53]
    W. Taylor, String field theory, hep-th/0605202 [SPIRES].
  54. [54]
    I.V. Volovich, p-adic string, Class. Quant. Grav. 4 (1987) L83 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  55. [55]
    L. Brekke, P.G.O. Freund, M. Olson and E. Witten, Nonarchimedean string dynamics, Nucl. Phys. B 302 (1988) 365 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  56. [56]
    P.H. Frampton and Y. Okada, Effective scalar field theory of p-adic string, Phys. Rev. D 37 (1988) 3077 [SPIRES].ADSMathSciNetGoogle Scholar
  57. [57]
    V.S. Vladimirov, I.V. Volovich and E.I. Zelenov, p-adic analysis and mathematical physics, World Scientific, Singapore (1994) [SPIRES].Google Scholar
  58. [58]
    B. Dragovich, A.Y. Khrennikov, S.V. Kozyrev and I.V. Volovich, On p-adic mathematical physics, P-Adic Numbers Ultrametric Anal. Appl. 1 (2009) 1 [arXiv:0904.4205] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  59. [59]
    A.A. Starobinsky, Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations, Phys. Lett. B 117 (1982) 175 [SPIRES].ADSGoogle Scholar
  60. [60]
    I.Y. Aref’eva, B. Dragovich, P.H. Frampton and I.V. Volovich, Wave function of the universe and p-adic gravity, Int. J. Mod. Phys. A 6 (1991) 4341 [SPIRES].ADSMathSciNetGoogle Scholar
  61. [61]
    S. Weinberg, Effective field theory for inflation, Phys. Rev. D 77 (2008) 123541 [arXiv:0804.4291] [SPIRES].ADSMathSciNetGoogle Scholar
  62. [62]
    R. Kallosh, J.U. Kang, A.D. Linde and V. Mukhanov, The new ekpyrotic ghost, JCAP 04 (2008) 018 [arXiv:0712.2040] [SPIRES].ADSMathSciNetGoogle Scholar
  63. [63]
    V.S. Vladimirov and Y.I. Volovich, On the nonlinear dynamical equation in the p-adic string theory, Theor. Math. Phys. 138 (2004) 297 [math-ph/0306018] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  64. [64]
    V.S. Vladimirov, On the equation of the p-adic open string for the scalar tachyon field, Izv. Math. 69 (2005) 487 [math-ph/0507018] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  65. [65]
    D.V. Prokhorenko, On some nonlinear integral equation in the (super)string theory, math-ph/0611068 [SPIRES].
  66. [66]
    L.V. Joukovskaya, Iterative method for solving nonlinear integral equations describing rolling solutions in string theory, Theor. Math. Phys. 146 (2006) 335 [arXiv:0708.0642] [SPIRES].CrossRefMATHGoogle Scholar
  67. [67]
    V.S. Vladimirov, On the equations for p-adic closed and open strings, p-Adic Numbers Ultrametric Anal. Appl. 1 (2009) 79. CrossRefMATHMathSciNetGoogle Scholar
  68. [68]
    P. Górka, H. Prado and E.G. Reyes, Functional calculus via Laplace transform and equations with infinitely many derivatives, J. Math. Phys. 51 (2010) 103512.CrossRefADSMathSciNetGoogle Scholar
  69. [69]
    H.T. Davis, The theory of linear operators from the standpoint of differential equations of infinite order, Principia Press, Bloomington U.S.A. (1936).Google Scholar
  70. [70]
    R.D. Carmichael, Linear differential equations of infinite order, Bull. Am. Math. Soc. 42 (1936) 193.CrossRefGoogle Scholar
  71. [71]
    L. Carleson, On infinite differential equations with constant coefficients. I, Math. Scand. 1 (1953) 31.MATHMathSciNetGoogle Scholar
  72. [72]
    L. Hörmander, The analysis of linear partial differential operators. Vol. I: Distribution theory and Fourier analysis, Springer-Verlag (1983).Google Scholar
  73. [73]
    L. Hörmander, The analysis of linear partial differential operators. Vol. II: Differential operators with constant coefficients, Springer-Verlag (1983).Google Scholar
  74. [74]
    L. Hörmander, The analysis of linear partial differential operators. Vol. III: Pseudo-differential operators, Springer-Verlag (1985).Google Scholar
  75. [75]
    L. Hörmander, The analysis of linear partial differential operators. Vol. IV: Fourier integral operators, Springer-Verlag (1985).Google Scholar
  76. [76]
    K.A. Khachatryan, Solubility of a class of the second-order integro-differential equations with monotone non-linearity on a semi-axis, Izv. Math. 74 (2010) 1069. CrossRefMATHMathSciNetGoogle Scholar
  77. [77]
    A. Pais and G.E. Uhlenbeck, On field theories with nonlocalized action, Phys. Rev. 79 (1950) 145 [SPIRES].CrossRefMATHADSMathSciNetGoogle Scholar
  78. [78]
    N. Moeller and B. Zwiebach, Dynamics with infinitely many time derivatives and rolling tachyons, JHEP 10 (2002) 034 [hep-th/0207107] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  79. [79]
    Y.I. Volovich, Numerical study of nonlinear equations with infinite number of derivatives, J. Phys. A 36 (2003) 8685 [math-ph/0301028] [SPIRES].ADSMathSciNetGoogle Scholar
  80. [80]
    I.Y. Aref’eva, L.V. Joukovskaya and A.S. Koshelev, Time evolution in superstring field theory on non-BPS brane. I: Rolling tachyon and energy-momentum conservation, JHEP 09 (2003) 012 [hep-th/0301137] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  81. [81]
    V.A. Fock, The eigen-time in classical and quantum mechanics (in German), Izv. Akad. Nauk SSSR 4–5 (1937) 551 [Phys. Zs. Sowjet. 12 (1937) 404] [SPIRES].Google Scholar
  82. [82]
    R.P. Feynman, Mathematical formulation of the quantum theory of electromagnetic interaction, Phys. Rev. 80 (1950) 440 [SPIRES].CrossRefMATHADSMathSciNetGoogle Scholar
  83. [83]
    D.A. Eliezer and R.P. Woodard, The problem of nonlocality in string theory, Nucl. Phys. B 325 (1989) 389 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  84. [84]
    V.S. Vladimirov, Equations of mathematical physics, Nauka, Moscow U.S.S.R. (1971).Google Scholar
  85. [85]
    M.A. Evgrafov, Analitical functions, Nauka, Moscow U.S.S.R. (1965).Google Scholar
  86. [86]
    N.N. Bogolyubov and Y.A. Mitropolski, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York U.S.A. (1961).Google Scholar
  87. [87]
    A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99 [SPIRES].ADSGoogle Scholar
  88. [88]
    A.H. Guth, The inflationary universe: a possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347 [SPIRES].ADSGoogle Scholar
  89. [89]
    A.D. Linde, A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. B 108 (1982) 389 [SPIRES].ADSMathSciNetGoogle Scholar
  90. [90]
    A. Albrecht and P.J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48 (1982) 1220 [SPIRES].CrossRefADSGoogle Scholar
  91. [91]
    A.D. Linde, Chaotic inflation, Phys. Lett. B 129 (1983) 177 [SPIRES].ADSMathSciNetGoogle Scholar
  92. [92]
    A.D. Linde, Initial conditions for inflation, Phys. Lett. B 162 (1985) 281 [SPIRES].ADSGoogle Scholar
  93. [93]
    R.P. Woodard, Generalizing Starobinskii’s formalism to Yukawa theory and to scalar QED, J. Phys. Conf. Ser. 68 (2007) 012032 [gr-qc/0608037] [SPIRES].CrossRefADSGoogle Scholar
  94. [94]
    I.V. Volovich, Randomness in classical mechanics and quantum mechanics, Found. Phys. 41 (2011) 516.CrossRefMATHADSMathSciNetGoogle Scholar
  95. [95]
    I.V. Volovich, Time irreversibility problem and functional formulation of classical mechanics, arXiv:0907.2445.
  96. [96]
    L. Accardi, Y.G. Lu and I.V. Volovich, Quantum theory and its stochastic limit, Springer (2002).Google Scholar
  97. [97]
    L.E. Reichl, The transition to chaos, Springer (2004).Google Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

Personalised recommendations