From the early to the late time universe within \(f(T,\mathcal{T})\) gravity

  • S. B. Nassur
  • M. J. S. Houndjo
  • M. E. Rodrigues
  • A. V. Kpadonou
  • J. Tossa
Original Article


In this paper we perform the reconstruction scheme of the gravitational action within \(f(T,\mathcal{T})\) gravity, where \(T\) and \(\mathcal{T}\) denote the torsion scalar and the trace of the energy momentum tensor, respectively. We particularly focus our attention on the case where the algebraic function \(f(T,\mathcal{T})\) is decomposed as a sum of two functions \(f_{1}(T)\) and \(f_{2}(\mathcal{T})\), i.e., \(f(T,\mathcal{T})=f_{1}(T)+f_{2}(\mathcal{T})\). The description is essentially based on the scale factor and then, we consider two interesting and realistic expressions of this parameter and reconstruct the action corresponding to each phase of the universe. Our results show that some \(f(T,\mathcal{T})\) models are able to describe the evolution of the universe from the inflation phase to the late time dark energy dominated phase.


Modified gravity Reconstruction 



S.B. Nassur thanks DAAD for financial support. M.J.S. Houndjo, V.A. Kpadonou and J. Tossa would like to thank Ecole Normale Supérieure Natitingou for partial financial backing during the elaboration of this work. M.E. Rodrigues thanks UFPA, Edital 04/2014 PROPESP, and CNPq Edital MCTI/CNPQ/Universal 14/2014, for partial financial support.


  1. Amorós, J., de Haro, J., Odintsov, S.D.: Phys. Rev. D, Part. Fields 87, 104037 (2013). arXiv:1305.2344 [gr-qc] CrossRefADSGoogle Scholar
  2. Bamba, K.: In: The Casimir Effect and Cosmology, pp. 142–152. Tomsk State Pedagogical University, Tomsk (2008). arXiv:0904.2655v1 [hep-th] Google Scholar
  3. Bamba, K.: (2012). arXiv:1202.4317v1 [gr-qc]
  4. Bamba, K., Geng, C., Lee, C., Luo, L.: J. Cosmol. Astropart. Phys. 1101, 021 (2011). arXiv:1011.0508v2 [astro-ph.CO] CrossRefADSGoogle Scholar
  5. Bamba, K., Capozziello, S., Nojiri, S., Odintsov, S.D.: Astrophys. Space Sci. 342, 155–228 (2012). arXiv:1205.3421v3 [gr-qc] CrossRefADSGoogle Scholar
  6. Bamba, K., Myrzakulov, R., Nojiri, S., Odintsov, S.D.: Phys. Rev. D, Part. Fields 85, 104036 (2013). arXiv:1202.4057v3 [gr-qc] CrossRefADSGoogle Scholar
  7. Basilakos, S., Capozziello, S., De Laurentis, M., Paliathanasis, A., Tsamparlis, M.: (2013). arXiv:1311.2173v1 [gr-qc]
  8. Davis, T.M., et al.: Astrophys. J. 666, 716 (2007). arXiv:astro-ph/0701510 CrossRefADSGoogle Scholar
  9. Dunkley, J., et al. (WMAP Collaboration): Astrophys. J. Suppl. Ser. 180, 306–329 (2009). arXiv:0803.0586 [astro-ph] CrossRefADSGoogle Scholar
  10. Harko, T., Lobo, F.S.N., Nojiri, S., Odintsov, S.D.: Phys. Rev. D 84, 024020 (2011). arXiv:1104.2669v2 [gr-qc] CrossRefADSGoogle Scholar
  11. Harko, T., Lobo, F.S.N., Otalora, G., Saridakis, E.N.: J. Cosmol. Astropart. Phys. 12, 021 (2014). arXiv:1405.0519v3 [gr-qc] CrossRefADSGoogle Scholar
  12. Houndjo, M.J.S.: Int. J. Mod. Phys. D 21, 1250003 (2012). arXiv:1107.3887v4 [astro-ph.Co] CrossRefADSMathSciNetGoogle Scholar
  13. Kiani, F., Nozari, K.: Phys. Lett. B 728, 554–561 (2014). arXiv:1309.1948v3 [gr-qc] CrossRefADSGoogle Scholar
  14. Komatsu, E., et al. (WMAP Collaboration): Astrophys. J. Suppl. Ser. 180, 330–376 (2009). arXiv:0803.0547 [astro-ph] CrossRefADSGoogle Scholar
  15. Komatsu, E., Smith, K.M., Dunkley, J., Bennett, C.L., Gold, B., Hinshaw, G., Jarosik, N., Larson, D., Nolta, M.R., Page, L., Spergel, D.N., Halpern, M., Hill, R.S., Kogut, A., Limon, M., Mayer, S.S., Odegard, N., Tucker, G.S., Weiland, J.L., Wollack, E., Right, E.N.: Astrophys. J. Suppl. Ser. 192, 18 (2011). arXiv:1001.4538v3 [astro-ph.CO] CrossRefADSGoogle Scholar
  16. Liddle, A.: An Introduction to Modern Cosmology, 2nd edn. Wiley, New York (2003) Google Scholar
  17. Liddle, A.R., Lyth, D.H.: Cosmological Inflation and Large-Scale Structure. Cambridge University Press, Cambridge (2006) Google Scholar
  18. Linder, E.V.: Phys. Rev. D 81, 127301 (2010). arXiv:1005.3039v2 [astro-ph.CO] CrossRefADSGoogle Scholar
  19. Momeni, D., Myrzakulov, R.: Int. J. Geom. Methods Mod. Phys. 11, 1450077 (2014). arXiv:1405.5863 [gr-qc]. doi: 10.1142/s0219887814500777 CrossRefMathSciNetGoogle Scholar
  20. Nojiri, S., Odintsov, S.D.: J. Phys. Conf. Ser. 66, 012005 (2007). arXiv:hep-th/0611071v2 CrossRefADSGoogle Scholar
  21. Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59–144 (2011). arXiv:1011.0544v4 [gr-qc] CrossRefADSMathSciNetGoogle Scholar
  22. Rodrigues, M.E., Houndjo, M.J.S., Sáez-Gómez, D., Rahaman, F.: Phys. Rev. D 86, 104059 (2012). arXiv:1209.4859v3 [gr-qc] CrossRefADSGoogle Scholar
  23. Sadeghi, J., Amani, A.R., Tahmasbi, N.: Astrophys. Space Sci. 348, 559–564 (2013). arXiv:1308.5308v1 [gr-qc]. doi: 10.1007/s10509-013-1579-y CrossRefADSGoogle Scholar
  24. Starobinsky, A.A.: Gravit. Cosmol. 6, 157–163 (2000). arXiv:astro-ph/9912054v1 ADSMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • S. B. Nassur
    • 1
  • M. J. S. Houndjo
    • 1
    • 2
  • M. E. Rodrigues
    • 3
  • A. V. Kpadonou
    • 1
    • 4
  • J. Tossa
    • 1
  1. 1.Institut de Mathématiques et de Sciences Physiques (IMSP)Porto-NovoBenin
  2. 2.Faculté des Sciences et Techniques de NatitingouUniversité de ParakouParakouBenin
  3. 3.Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do ParáCampus Universitário de AbaetetubaAbaetetubaBrazil
  4. 4.Ecole Normale Supérieure de NatitingouUniversité de ParakouParakouBenin

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