Abstract.
In this paper, we investigate the cosmological evolution in a new modified teleparallel gravity that connects both f(T) and f(R) theories with a boundary term B, called f(T,B) gravity. To this purpose, we assume flat Friedmann-Robertson-Walker (FRW) geometry filled with perfect fluid matter contents. We formulate the general energy constraints for two cases in this gravity: one is for a general function of f(T,B), and the other is for a particular form of it given by - T + F(B). Further, we explore the validity of these energy bounds by specifying different forms of f(T, B) and F(B) functions obtained by the reconstruction scheme for de Sitter, power-law, \(\Lambda\) CDM and phantom cosmological models. In order to constrain the free model parameters, we examine these energy bounds with the help of region graphs. We also explore the evolution of the effective equation of state (EoS) \(\omega_{\rm eff}\) for both cases and compare theoretical results with the observational data. It is found that the effective EoS represents the phantom phase or the quintessence state of accelerating universe in all cases, which is consistent with observational data.
Similar content being viewed by others
References
S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007)
S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011)
S. Capozziello, V. Faraoni, Beyond Einstein Gravity (Springer, Dordrecht, 2010)
S. Capozziello, M.D. Laurentis, Phys. Rep. 509, 167 (2011)
K. Bamba, S. Capozziello, S. Nojiri, S.D. Odintsov, Astrophys. Space Sci. 342, 155 (2012)
A. Joyce, B. Jain, J. Khoury, M. Trodden, Phys. Rep. 568, 1 (2015)
K. Koyama, Rep. Prog. Phys. 79, 046902 (2016)
K. Bamba, S.D. Odintsov, Symmetry 7, 220 (2015)
S. Nojiri, S.D. Odintsov, V.K. Oikonomou, Phys. Rep. 692, 1 (2017)
K. Bamba, S. Nojiri, S.D. Odintsov, J. Cosmol. Astropart. Phys. 08, 045 (2008)
M. Sharif, M. Zubair, J. Cosmol. Astropart. Phys. 03, 028 (2012)
K. Bamba, S.D. Odintsov, L. Sebastiani, S. Zerbini, Eur. Phys. J. C 67, 295 (2010)
H. Weyl, Sitzungsber. Preuss. Akad. Wissensch. 1918, 465 (1918)
L.O. Raifeartaigh, The Dawning of Gauge Theory (Princeton University Press, Princeton, 1998)
L.O. Raifeartaigh, N. Straumann, Rev. Mod. Phys. 72, 1 (2000)
A. Einstein, Math. Ann. 102, 685 (1930) (for an English translation, together with three previous essays, see A. Unzicker, T. Case, Unified field theory based on Riemannian metrics and distant parallelism
T. Kaluza, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1921, 966 (1921)
O. Klein, Z. Phys. 37, 895 (1926)
E. Cartan, Ann. Sci. Éc. Norm. Super. 40, 325 (1923)
E. Cartan, Ann. Sci. Éc. Norm. Super. 41, 1 (1924)
C. Møller, K. Dan. Vidensk. Selsk. Mat. Fys. Skr. 1, 10 (1961)
C. Møller, K. Dan. Vidensk. Selsk. Mat. Fys. Skr. 89, 13 (1978)
C. Pellegrini, J. Plebanski, K. Dan. Vidensk. Selsk. Mat. Fys. Skr. 2, 2 (1962)
Y.M. Cho, Phys. Rev. D 14, 2521 (1976)
K. Hayashi, T. Shirafuji, Phys. Rev. D 19, 3524 (1979)
K. Hayashi, T. Nakano, Prog. Theor. Phys. 38, 491 (1967)
K. Hayashi, Nuovo Cimento A 16, 639 (1973)
K. Hayashi, Phys. Lett. B 69, 441 (1977)
R. Aldrovandi, J.G. Pereira, Teleparallel Gravity: An Introduction, in Fundamental Theories of Physics, Vol. 173 (Springer Dodrecht, Heidelberg, 2013)
J.W. Maluf, Ann. Phys. 525, 339 (2013) arXiv:1303.3897
R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007)
G.R. Bengochea, R. Ferraro, Phys. Rev. D 79, 124019 (2009)
E.V. Linder, Phys. Rev. D 81, 127301 (2010)
T. Wang, Phys. Rev. D 84, 024042 (2011)
J.B. Dent, S. Dutta, E.N. Saridakis, J. Cosmol. Astropart. Phys. 01, 009 (2011)
C.G. Bohmer, T. Harko, F.S.N. Lobo, Phys. Rev. D 85, 044033 (2012)
Y.P. Wu, C.Q. Geng, J. High Energy Phys. 11, 142 (2012)
A. Aviles, A. Bravetti, S. Capozziello, O. Luongo, Phys. Rev. D 87, 064025 (2013)
S. Paliathanasis et al., Phys. Rev. D 89, 104042 (2014)
J.T. Wheeler, Nucl. Phys. B 268, 737 (1986)
I.S. Nojiri, S.D. Odintsov, M. Sasaki, Phys. Rev. D 71, 123509 (2005)
A. De Felice, S. Tsujikawa, Phys. Rev. D 80, 063516 (2009)
M. Zubair, Int. J. Mod. Phys. D 25, 1650057 (2016)
M. Zubair, G. Abbas, Astrophys. Space Sci. 361, 27 (2016)
M. Zubair, Adv. High Energy Phys. 2015, 292767 (2015)
G. Kofinas, E.N. Saridakis, Phys. Rev. D 90, 084044 (2014)
G. Kofinas, G. Leon, E.N. Saridakis, Class. Quantum Grav. 31, 175011 (2014)
S. Bahamonde, C.G. Bohmer, Eur. Phys. J. C 76, 578 (2016)
T. Harko, F.S.N. Lobo, G. Otalora, E.N. Saridakis, Phys. Rev. D 89, 124036 (2014)
M. Zubair, S. Waheed, Astrophys. Space Sci. 355, 361 (2015)
M. Zubair, S. Waheed, Astrophys. Space Sci. 360, 68 (2015)
Y.F. Cai, S. Capozziello, M.D. Laurentis, E.N. Saridakis, Rep. Prog. Phys. 79, 106901 (2016)
K. Bamba, R. Myrzakulov, S. Nojiri, S.D. Odintsov, Phys. Rev. D 85, 104036 (2012)
T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010)
A.D. Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010)
R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007)
B. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 064035 (2011)
T.P. Sotiriou, B. Li, J.D. Barrow, Phys. Rev. D 83, 104030 (2011)
S. Bahamonde, C.G. Bohmer, M. Wright, Phys. Rev. D 92, 104042 (2015)
S. Bahamonde, M. Zubair, G. Abbas, Phys. Dark Univ. 19, 78 (2018)
J. Santos et al., Phys. Rev. D 76, 083513 (2007)
J. Santos, M.J. Reboucas, J.S. Alcaniz, Int. J. Mod. Phys. D 19, 1315 (2010)
Di Liu, M.J. Reboucas, Phys. Rev. D 86, 083515 (2012)
N.M. Garcia, Phys. Rev. D 83, 104032 (2011)
Y.Y. Zhao, Eur. Phys. J. C 72, 1924 (2012)
O. Bertolami, M.C. Sequeira, Phys. Rev. D 79, 104010 (2009)
J. Wang et al., Phys. Lett. B 689, 133 (2010)
J. Wang, K. Liao, Class. Quantum Grav. 29, 215016 (2012)
K. Atazadeh, A. Khaleghi, H.R. Sepangi, Y. Tavakoli, Int. J. Mod. Phys. D 18, 1101 (2009)
M. Sharif, S. Waheed, Adv. High Energy Phys. 2013, 253985 (2013)
M. Sharif, M. Zubair, J. Phys. Soc. Jpn. 82, 014002 (2013)
M. Sharif, M. Zubair, J. High Energy Phys. 12, 079 (2013)
S. Waheed, M. Zubair, Astrophys. Space Sci. 359, 47 (2016)
M. Visser, C. Barceló, COSMO 99, 98 (2000)
M. Sharif, S. Rani, R. Myrzakulov, Eur. Phys. J. Plus 128, 123 (2013) E. Curiel, A Primer on Energy Conditions
S. Capozziello, V.F. Cardone, H. Farajollahi, A. Ravanpak, Phys. Rev. D 84, 043527 (2011)
G. Hinshw et al., Astrophys. J. Suppl. Ser. 208, 19 (2013)
P.A.R. Ade et al., Astron. Astrophys. 571, A1 (2014)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zubair, M., Waheed, S., Atif Fayyaz, M. et al. Energy constraints and the phenomenon of cosmic evolution in the f(T,B) framework. Eur. Phys. J. Plus 133, 452 (2018). https://doi.org/10.1140/epjp/i2018-12252-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2018-12252-2