Abstract
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.
Similar content being viewed by others
Change history
23 July 2019
In the original article Supriya Kar was listed as a co-author without his permission. The sole author of this article is Deobrat Singh.
16 July 2020
The author has retracted this article [1] because it significantly overlaps with a previously published article by Singh and Kar [2].
References
S. Perlmutter, et al., Supernova cosmology project collaboration. Astrophys. J. 517, 565 (1999). arXiv:[astro-ph/9812133]
Supernova Serach Team, (G.Riess et.al). Astrom. J. 116, 1009 (1998)
D.N. Spergel, et al., WMAP collaboration. Astrophys. J. Suppl. 148, 175 (2003)
D.J. Eisenstein, et al., SDSS collaboration. Astrophys. J. 633, 560 (2005)
K.N. Abazajian, et al., SDSS collaboration. Astrophys. J. Suppl. 182, 543 (2009)
P.A.R. Ade, et al., Planck collaboration. Astron. Astrophys. 571, A16 (2014)
E. J. Copeland, M. Sami, S. Tsujikawa, Dynamics of dark energy. Int. J. Mod. Phys. D. 15, 1753 (2006)
T. Clifton, P. G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rep. 513, 1 (2012)
H. S. Yang, Emergent geometry and quantum gravity. Mod. Phys. Lett. 25, 2381 (2010)
S. Candelas, G. T. Horowitz, A. Strominger, Vacuum configurations for superstrings. Nucl. Phys. 258, 46 (1985)
D. S. Freed, Determinants, torsion, and strings. Comm. Math. Phys. 107, 483 (1986)
C.G. Callan, R.C. Meyers, M.J. Perry, Black holes in string theory. Nucl. Phys. 311, 673 (1988/89)
D. Garfinkle, G.T. Horowitz, A. Strominger, Charged black holes in string theory. Phys. Rev. 43, 31403143 (1991)
S. B. Giddings, A. Strominger, Exact black five-branes in critical superstring theory. Phys. Rev. Lett. 67, 2930 (1991)
A. Sen, Strong–weak coupling duality in four-dimensional string theory. Int. J. Mod. Phys. 9, 3707 (1994)
E. Witten, String theory dynamics in various dimensions. Nucl. Phys. 443, 85 (1995)
J. Schwinger, On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951)
S. W. Hawking, Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)
C. Bachas, M. Porrati, Pair creation of open strings in an electric field. Phys. Lett. 296, 77 (1992)
M. Majumdar, A. -C. Davis, Cosmological creation of D-branes and anti-D-branes. JHEP. 03, 056 (2002)
T. W. B. Kibble, Topology of cosmic domains and strings. J. Phys. A: Math. Gen. 9, 1387 (1976)
T. W.B. Kibble, Some implications of a cosmological phase transition. Phys. Rep. 67, 183–199 (1980)
W. H. Zurek, Cosmological experiments in superfluid helium?. Nature. 317, 505 (1985)
W. H. Zurek, Cosmic strings in laboratory superfluids and the topological remnants of other phase transitions. Acta Phys. Pol. B. 24, 1301 (1993)
W. H. Zurek, Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177 (1996)
E. Alvarez, M.A.R. Osorio, Primordial superstrings and the origin of the Universe. Int. J. Theor. Phys. 28 (9), 949 (1989)
M. Gasperini, Astropart. Phys. 1, 317–339 (1993). arXiv:gr-qc/0105082
G. Veneziano, CERN-TH/98-43, arXiv:CERN-TH/2000-042
R. Durrer, et al., arXiv:astro-ph/0010408v3
R.H. Brandenberger, arXiv:hep-th/0103156
J. Khoury, et al., arXiv:hep-th/0103239v3
P. Horava, and E. Witten, arXiv:hep-th/9603142
J.M. Hoff da Silva, R. da Rocha, Torsion effects in braneworld scenarios. Phys. Rev. D81, 024021 (2010)
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) 179801
A. K. Singh, K. P. Pandey, S. Singh, S. Kar, Discrete torsion, de Sitter tunneling vacua and AdS brane: U(1) gauge theory on D4-brane and an effective curvature. JHEP. 05, 033 (2013)
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 B2-field on a D4-brane. Phys. Rev. 88, 066001 (2013)
A. K. Singh, K. P. Pandey, S. Singh, S. Kar, Discrete torsion, (Anti) de Sitter D4-Brane and Tunneling. Nucl. Phys. 252-252, 241 (2014)
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)
D. Singh, R. Kapoor, S. Kar, Torsion geometries in U(1) gauge theory on D5-brane. Springer Proc. Phys. 174(77), 507–512 (2016). ISBN 978-3-319-25617-7
J. Polchinski, Dirichlet branes and Ramond-Ramond charges. Phys. Rev. Lett. 75, 4724 (1995)
A. Sen, Stable non-BPS states in string theory. JHEP. 9806, 007 (1998)
A. Sen, Tachyon condensation on the brane antibrane system. JHEP. 9808, 012 (1998)
N. Seiberg, E. Witten, String theory and noncommutative geometry. JHEP. 09, 032 (1999)
F. Quevedo, Lectures on string/brane cosmology. Class. Quant. Grav. 19, 5721 (2002)
G. Shiu, S. -H. H. Tye, Some aspects of brane inflation. Phys. Lett. 516, 421 (2001)
M. Mjaumdar, A. -C. Davis, D-brane Anti-brane annihilation in an expanding universe. JHEP. 0312, 012 (2003)
T. Padmanabhan, Emergent perspective of gravity and dark energy. Res. Aston. Astrophys. 12, 891 (2012)
R. -G. Cai, Emergence of space and spacetime dynamics of Friedmann-Robertson-Walker universe. JHEP. 11, 016 (2012)
P. Ratra, L. Peebles, Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D. 37 (12), 3406 (1988)
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)
I. Zlatev, L. Wang, P. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett. 82(5), 896–899 (1999)
J.P. Ostriker, P. Steinhardt, The quintessential universe. Sci. Am. 284(1), 46–53 (2001)
S. Chen, Q. Pan, J. Jing, Holographic superconductors in quin- tessence AdS black hole. Class. Quant. Grav. 30, 145001 (2013)
W.Y. Huan, R. Jun, Thermodynamic properties of Reissner-Nordström-de Sitter quintessence black holes. Chin. Phys. D. 22, 030402 (2013)
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)
K.P. Pandey, A.K. Singh, S. Singh, S. Kar, Quintessence and effective AdS brane geometries. Int. J. Mod. Phys. 30, 1550065 (2015)
L.D. Duffy, K. van Bibber, Axions as dark matter particles, Vol. 11 (2009)
P Sikivie, Dark matter axions. Int. J. Mod. Phys. 25(2003), 554–563 (2009)
Acknowledgments
The data used to support the findings of this study are included within the article.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Singh, D., Kar, S. RETRACTED ARTICLE: Emergent D-Instanton as a Source of Dark Energy. Braz J Phys 49, 249–255 (2019). https://doi.org/10.1007/s13538-019-00635-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13538-019-00635-y