Emergent D-Instanton as a Source of Dark Energy

  • Deobrat SinghEmail author
  • Supriya Kar
Particles and Fields


We revisit a non-perturbative formulation leading to a vacuum-created gravitational pair of \((3\bar {3})\)-brane by a Poincare dual higher form U(1) gauge theory on a D4-brane. In particular, the analysis has revealed a dynamical geometric torsion \(\mathcal {H}_{3}\) for an onshell Neveu-Schwarz (NS) form on a fat 4-brane. We argue that a D-instanton can be a viable candidate to incorporate the quintessence correction hidden to an emergent (3 + 1)-dimensional brane universe. It is shown that a dynamical non-perturbative correction may be realized with an axionic scalar QFT on an emergent anti-3-brane within a gravitational pair. The theoretical tool provokes thought to believe for an extra instantaneous dimension transverse to our classical brane-universe in an emergent scenario. Interestingly a D-instanton correction, sourced by an axion on an anti-3-brane, may serve as a potential candidate to explain the accelerated rate of expansion of our 3-brane universe and may provide a clue to the origin of dark energy.


Dark energy Instanton String theory Axion Big Bang 



The data used to support the findings of this study are included within the article.


  1. 1.
    S. Perlmutter, et al., Supernova cosmology project collaboration. Astrophys. J. 517, 565 (1999). arXiv:[astro-ph/9812133] ADSGoogle Scholar
  2. 2.
    Supernova Serach Team, (G.Riess Astrom. J. 116, 1009 (1998)Google Scholar
  3. 3.
    D.N. Spergel, et al., WMAP collaboration. Astrophys. J. Suppl. 148, 175 (2003)ADSGoogle Scholar
  4. 4.
    D.J. Eisenstein, et al., SDSS collaboration. Astrophys. J. 633, 560 (2005)ADSGoogle Scholar
  5. 5.
    K.N. Abazajian, et al., SDSS collaboration. Astrophys. J. Suppl. 182, 543 (2009)ADSGoogle Scholar
  6. 6.
    P.A.R. Ade, et al., Planck collaboration. Astron. Astrophys. 571, A16 (2014)Google Scholar
  7. 7.
    E. J. Copeland, M. Sami, S. Tsujikawa, Dynamics of dark energy. Int. J. Mod. Phys. D. 15, 1753 (2006)ADSMathSciNetzbMATHGoogle Scholar
  8. 8.
    T. Clifton, P. G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rep. 513, 1 (2012)ADSMathSciNetGoogle Scholar
  9. 9.
    H. S. Yang, Emergent geometry and quantum gravity. Mod. Phys. Lett. 25, 2381 (2010)ADSMathSciNetzbMATHGoogle Scholar
  10. 10.
    S. Candelas, G. T. Horowitz, A. Strominger, Vacuum configurations for superstrings. Nucl. Phys. 258, 46 (1985)ADSMathSciNetGoogle Scholar
  11. 11.
    D. S. Freed, Determinants, torsion, and strings. Comm. Math. Phys. 107, 483 (1986)ADSMathSciNetzbMATHGoogle Scholar
  12. 12.
    C.G. Callan, R.C. Meyers, M.J. Perry, Black holes in string theory. Nucl. Phys. 311, 673 (1988/89)Google Scholar
  13. 13.
    D. Garfinkle, G.T. Horowitz, A. Strominger, Charged black holes in string theory. Phys. Rev. 43, 31403143 (1991)MathSciNetGoogle Scholar
  14. 14.
    S. B. Giddings, A. Strominger, Exact black five-branes in critical superstring theory. Phys. Rev. Lett. 67, 2930 (1991)ADSMathSciNetzbMATHGoogle Scholar
  15. 15.
    A. Sen, Strong–weak coupling duality in four-dimensional string theory. Int. J. Mod. Phys. 9, 3707 (1994)ADSMathSciNetzbMATHGoogle Scholar
  16. 16.
    E. Witten, String theory dynamics in various dimensions. Nucl. Phys. 443, 85 (1995)ADSMathSciNetzbMATHGoogle Scholar
  17. 17.
    J. Schwinger, On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951)ADSMathSciNetzbMATHGoogle Scholar
  18. 18.
    S. W. Hawking, Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)ADSMathSciNetzbMATHGoogle Scholar
  19. 19.
    C. Bachas, M. Porrati, Pair creation of open strings in an electric field. Phys. Lett. 296, 77 (1992)MathSciNetGoogle Scholar
  20. 20.
    M. Majumdar, A. -C. Davis, Cosmological creation of D-branes and anti-D-branes. JHEP. 03, 056 (2002)ADSMathSciNetGoogle Scholar
  21. 21.
    T. W. B. Kibble, Topology of cosmic domains and strings. J. Phys. A: Math. Gen. 9, 1387 (1976)ADSzbMATHGoogle Scholar
  22. 22.
    T. W.B. Kibble, Some implications of a cosmological phase transition. Phys. Rep. 67, 183–199 (1980)ADSMathSciNetGoogle Scholar
  23. 23.
    W. H. Zurek, Cosmological experiments in superfluid helium?. Nature. 317, 505 (1985)ADSGoogle Scholar
  24. 24.
    W. H. Zurek, Cosmic strings in laboratory superfluids and the topological remnants of other phase transitions. Acta Phys. Pol. B. 24, 1301 (1993)Google Scholar
  25. 25.
    W. H. Zurek, Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177 (1996)ADSGoogle Scholar
  26. 26.
    E. Alvarez, M.A.R. Osorio, Primordial superstrings and the origin of the Universe. Int. J. Theor. Phys. 28 (9), 949 (1989)zbMATHGoogle Scholar
  27. 27.
    M. Gasperini, Astropart. Phys. 1, 317–339 (1993). arXiv:gr-qc/0105082 ADSGoogle Scholar
  28. 28.
    G. Veneziano, CERN-TH/98-43, arXiv:CERN-TH/2000-042
  29. 29.
    R. Durrer, et al., arXiv:astro-ph/0010408v3
  30. 30.
    R.H. Brandenberger, arXiv:hep-th/0103156
  31. 31.
    J. Khoury, et al., arXiv:hep-th/0103239v3
  32. 32.
    P. Horava, and E. Witten, arXiv:hep-th/9603142
  33. 33.
    J.M. Hoff da Silva, R. da Rocha, Torsion effects in braneworld scenarios. Phys. Rev. D81, 024021 (2010)ADSGoogle Scholar
  34. 34.
    J.M. Hoff da Silva, R. da Rocha, Braneworld remarks in Riemann–Cartan manifolds. Class. Quant. Grav. 26, 055007 (2009). Erratum: Class.Quant.Grav. 26 (2009) 179801ADSMathSciNetzbMATHGoogle Scholar
  35. 35.
    A. K. Singh, K. P. Pandey, S. Singh, S. Kar, Discrete torsion, de Sitter tunneling vacua and AdS brane: U(1) gauge theory on D 4-brane and an effective curvature. JHEP. 05, 033 (2013)ADSzbMATHGoogle Scholar
  36. 36.
    A.K. Singh, K.P. Pandey, S. Singh, S. Kar, Emergent Schwarzschild and Reissner-Nordstrom black holes in four dimensions: An effective curvature sourced by a B 2-field on a D 4-brane. Phys. Rev. 88, 066001 (2013)Google Scholar
  37. 37.
    A. K. Singh, K. P. Pandey, S. Singh, S. Kar, Discrete torsion, (Anti) de Sitter D 4-Brane and Tunneling. Nucl. Phys. 252-252, 241 (2014)Google Scholar
  38. 38.
    R. Kapoor, S. Kar, D. Singh, Quantum effects in topological and Schwarzschild de Sitter brane: Aspects of torsion on \((D\overline {D})_{4}\)-brane universe. Int. J. Mod. Phys. D24(2), 1550015 (2015)ADSzbMATHGoogle Scholar
  39. 39.
    D. Singh, R. Kapoor, S. Kar, Torsion geometries in U(1) gauge theory on D 5-brane. Springer Proc. Phys. 174(77), 507–512 (2016). ISBN 978-3-319-25617-7Google Scholar
  40. 40.
    J. Polchinski, Dirichlet branes and Ramond-Ramond charges. Phys. Rev. Lett. 75, 4724 (1995)ADSMathSciNetzbMATHGoogle Scholar
  41. 41.
    A. Sen, Stable non-BPS states in string theory. JHEP. 9806, 007 (1998)ADSMathSciNetGoogle Scholar
  42. 42.
    A. Sen, Tachyon condensation on the brane antibrane system. JHEP. 9808, 012 (1998)ADSMathSciNetzbMATHGoogle Scholar
  43. 43.
    N. Seiberg, E. Witten, String theory and noncommutative geometry. JHEP. 09, 032 (1999)ADSMathSciNetzbMATHGoogle Scholar
  44. 44.
    F. Quevedo, Lectures on string/brane cosmology. Class. Quant. Grav. 19, 5721 (2002)MathSciNetzbMATHGoogle Scholar
  45. 45.
    G. Shiu, S. -H. H. Tye, Some aspects of brane inflation. Phys. Lett. 516, 421 (2001)zbMATHGoogle Scholar
  46. 46.
    M. Mjaumdar, A. -C. Davis, D-brane Anti-brane annihilation in an expanding universe. JHEP. 0312, 012 (2003)ADSMathSciNetGoogle Scholar
  47. 47.
    T. Padmanabhan, Emergent perspective of gravity and dark energy. Res. Aston. Astrophys. 12, 891 (2012)ADSGoogle Scholar
  48. 48.
    R. -G. Cai, Emergence of space and spacetime dynamics of Friedmann-Robertson-Walker universe. JHEP. 11, 016 (2012)ADSMathSciNetGoogle Scholar
  49. 49.
    P. Ratra, L. Peebles, Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D. 37 (12), 3406 (1988)ADSGoogle Scholar
  50. 50.
    R.R. Caldwell, R. Dave, P.J. Steinhardt, Cosmological imprint of an energy component with general equation-of-state. Phys. Rev. Lett. 80(8), 1582–1585 (1998)ADSzbMATHGoogle Scholar
  51. 51.
    I. Zlatev, L. Wang, P. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett. 82(5), 896–899 (1999)ADSGoogle Scholar
  52. 52.
    J.P. Ostriker, P. Steinhardt, The quintessential universe. Sci. Am. 284(1), 46–53 (2001)ADSGoogle Scholar
  53. 53.
    S. Chen, Q. Pan, J. Jing, Holographic superconductors in quin- tessence AdS black hole. Class. Quant. Grav. 30, 145001 (2013)ADSzbMATHGoogle Scholar
  54. 54.
    W.Y. Huan, R. Jun, Thermodynamic properties of Reissner-Nordström-de Sitter quintessence black holes. Chin. Phys. D. 22, 030402 (2013)Google Scholar
  55. 55.
    K. P. Pandey, A. K. Singh, S. Singh, R. Kapoor, S. Kar, Quintessence and effective RN de Sitter brane geometries. Eur. Phys. J. 74(11), 3173 (2014)ADSGoogle Scholar
  56. 56.
    K.P. Pandey, A.K. Singh, S. Singh, S. Kar, Quintessence and effective AdS brane geometries. Int. J. Mod. Phys. 30, 1550065 (2015)ADSzbMATHGoogle Scholar
  57. 57.
    L.D. Duffy, K. van Bibber, Axions as dark matter particles, Vol. 11 (2009)Google Scholar
  58. 58.
    P Sikivie, Dark matter axions. Int. J. Mod. Phys. 25(2003), 554–563 (2009)ADSzbMATHGoogle Scholar

Copyright information

© Sociedade Brasileira de Física 2019

Authors and Affiliations

  1. 1.Department of Physics & AstrophysicsUniversity of DelhiNew DelhiIndia
  2. 2.Department of Applied ScienceMadhav Institute of Technology and ScienceGwaliorIndia

Personalised recommendations