Abstract.
We show that the description of the spacetime in terms of backward-forward extension of its corresponding metric leads to the geometric origin of a small cosmological constant. The nonlocal cosmological constant appears in the Einstein’s field equation and its mathematical expression depends on the nonlocal metric, Ricci scalar and the infinitesimal nonlocal parameter introduced in the theory. The modified theory has interesting consequences in FRW cosmology, mainly a nonsingular universe, the occurrence of a late-time accelerated expansion of the universe and an early universe dominated by a negative energy density and a positive pressure. Our model can explain the acceleration of the universe without a fine-tuned cosmological constant \(\Lambda\).
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References
B. Mashhoon, Phys. Rev. A 47, 4498 (1993)
N. Bohr, L. Rosenfeld, K. Dan, Vidensk. Selsk. Mat. Fys. Medd. 12, 8 (1933) (translated in Quantum Theory and Measurement
C. Cremaschini, M. Tessarotto, Eur. Phys. J. Plus 126, 42 (2011)
C. Cremaschini, M. Tessarotto, Eur. Phys. J. Plus 126, 63 (2011)
M. Tessarotto, C. Cremaschini, Adv. Math. Phys. 2016, 9619326 (2016)
F.W. Hehl, B. Mashhoon, Phys. Rev. D 79, 064028 (2009)
C. Chicone, B. Mashhoon, Class. Quantum Grav. 33, 075005 (2016)
F.W. Hehl, B. Mashhoon, Phys. Lett. B 673, 279 (2009)
N.C. Tsamis, R.P. Woodard, J. Cosmol. Astropart. Phys. 09, 008 (2014)
F. Briscese, A. Marcianò, L. Modesto, E.N. Saridakis, Phys. Rev. D 87, 083507 (2007)
A.O. Barvinsky, Phys. Rev. D 85, 104018 (2012)
I. Dimitrijevic, B. Dragovich, J. Stankovic, A.S. Koshelev, Z. Rakic, Springer Proc. Math. Stat. 191, 35 (2016)
M. Blagojevic, F.W. Hehl (Editors), Gauge Theories of Gravitation (Imperial College Press, London, UK, 2013)
R. Aldrovandi, J.G. Pereira, Teleparallel Gravity: An Introduction (Springer, New York, NY, USA, 2013)
F.W. Hehl, B. Mashhoon, Phys. Rev. D 79, 064028 (2009)
L. Nottale, Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity (World Scientific, 1993)
R.A. El-Nabulsi, Qual. Theory Dyn. Syst. 13, 149 (2014)
R.A. El-Nabulsi, Qual. Theory Dyn. Syst. 16, 223 (2017)
Z.-Y. Li, J.-L. Fu, L.-Q. Chen, Phys. Lett. A 374, 106 (2009)
R.A. El-Nabulsi, Anal. Univ. Vest Tim. LIV1, 139 (2016)
R.A. El-Nabulsi, D.F.M. Torres, J. Math. Phys. 49, 053521 (2008)
J. Cresson, J. Math. Phys. 48, 033504 (2007)
J.A.K. Suykens, Phys. Lett. A 373, 1201 (2009)
J. Shao, N. Makri, J. Phys. Chem. 103, 9479 (1999)
C.-Y. Hsieh, R. Kapral, J. Chem. Phys. 137, 22A507 (2012)
G. Cusin, S. Foffa, M. Maggiore, M. Mancarella, Phys. Rev. D 93, 043006 (2016)
R. Utiyama, B.S. DeWitt, J. Math. Phys. 3, 608 (1962)
E. Pechlaner, R. Sexl, Commun. Math. Phys. 2, 165 (1966)
K.S. Stelle, Gen. Relativ. Gravit. 9, 353 (1978)
M. Farhoudi, Gen. Relativ. Gravit. 38, 1261 (2006)
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman, San Francisco, 1973)
S.M. Carroll, Spacetime and Geometry (Addison-Wesley, 2004)
S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (J. Wiley & Sons, 1972)
M. Szydlowski, A. Stachowski, J. Cosmol. Astropart. Phys. 10, 066 (2015)
S.M. Carroll, Why is the universe accelerating?, in Measuring and Modeling the Universe, edited by W.L. Freedman (Cambridge University Press, Cambridge, 2003)
S. Rani, A. Altaibayeva, M. Shahalam, J.K. Singh, R. Myrzakulov, J. Cosmol. Astropart. Phys. 03, 031 (2015)
A. Dolgov, V. Halenka, I. Tkachev, J. Cosmol. Astropart. Phys. 10, 047 (2014)
V. Sahni, T.D. Saini, A. Starobinsky, U. Alam, JETP Lett. 77, 201 (2003)
U. Debnath, Class. Quantum Grav. 25, 205019 (2008)
R.J. Nemiroff, R. Joshi, B.R. Patla, J. Cosmol. Astropart. Phys. 06, 006 (2015)
A. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic Publishers, 1990)
S. Ray, M. Khlopov, U. Mukhopadhyay, P.P. Ghosh, Int. J. Theor. Phys. 50, 939 (2011)
I.A. Aref’eva, S. Yu. Vernov, A.S. Koshelev, Theor. Math. Phys. 148, 895 (2006)
I. Dimitrijevic, B. Dragovich, J. Grujic, Z. Rakic, Publ. Inst. Math. 94, 187 (2013)
J. Grujic, Krag. J. Math. 39, 73 (2015)
H. Azri, A. Bounames, Gen. Relativ. Gravit. 44, 2547 (2012)
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El-Nabulsi, R.A. Nonlocal modified Einstein’s field equation and geometric origin of a small cosmological constant. Eur. Phys. J. Plus 133, 4 (2018). https://doi.org/10.1140/epjp/i2018-11841-3
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DOI: https://doi.org/10.1140/epjp/i2018-11841-3