Abstract
Under the premise that the current observations of the cosmic microwave background radiation set a very stringent limit to the anisotropy of the universe, we consider an anisotropic model in the presence of a barotropic perfect fluid and a homogeneous scalar field, which transits to a flat FRW cosmology for late times in a dust epoch, presenting an accelerated volume expansion. Furthermore, the scalar field is identified with a varying cosmological term via \(V(\phi (t))=2\Lambda (t)\). Exact solutions to the EKG system are obtained by proposing an anisotropic extension of the scaling solutions scenario: \(\rho \sim \eta ^{-n}, \rho _{\phi }\sim \eta ^{-{m}}\), with \(\eta ^{3}={a}_{1}{a}_{2}{a}_{3}\) the volume function of the anisotropic model (\({a_{1}}, {a_{2}}, {a_{3}}\) being the scale factors).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdel, A.M.M.: Gen. Relativ. Gravit. 22, 655 (1990)
Akarsu, Ö., et al.: Phys. Rev. D 100, 023532 (2019)
Amirhashchi, H.: Phys. Rev. D 97, 063515 (2018)
Amirhashchi, H., Amirhashchi, S.: Phys. Rev. D 99, 023516 (2019)
Arbab, A.I.: Gen. Relativ. Gravit. 29, 61 (1997)
Arbab, A.I.: Spacetime and Substance, vol. 1, p. 39 (2001)
Arbab, A.I.: Class. Quantum Gravity 20, 93 (2003)
Arbab, A.I.: Astrophys. Space Sci. 291, 141 (2004)
Arbab, A.I., Abdel-Rahaman, A.M.M.: Phys. Rev. D 50, 7725 (1994)
Bal, R., Singh, J.P.: Int. J. Theor. Phys. 47, 3288 (2008)
Bali, R.: Int. J. Theor. Phys. 50, 3043 (2011)
Bali, R., Jain, V.C.: Pramana J. Phys. 59, 1 (2002)
Beesham, A.: Phys. Rev. D 48, 3539 (1993)
Beesham, A.: Gen. Relativ. Gravit. 26, 159 (1994)
Belinchón, J.A.: Int. J. Mod. Phys. A 23, 5021 (2008)
Belinskii, V.A., Khalatnikov, I.M.: Sov. Phys. JETP 63, 1121 (1972)
Birkel, M., Sarkar, S.: Astropart. Phys. 6, 197 (1997)
Burd, A.B., Barrow, J.D.: Nucl. Phys. B 308, 929 (1988)
Bylan, S., Scialom, D.: Phys. Rev. D 57, 6065 (1998)
Carneiro, S., Lima, J.A.S.: Int. J. Mod. Phys. A 20, 2465 (2005)
Carvalho, J.C., et al.: Phys. Rev. D 46, 2404 (1992)
Chen, W., Wu, Y.S.: Phys. Rev. D 41, 695 (1990)
Copeland, E.J., et al.: Phys. Rev. D 57, 4686 (1998)
Cunha, J.V., Santos, R.C.: Int. J. Mod. Phys. D 13, 1321 (2004)
Espinoza García, A., et al.: Int. J. Theor. Phys. 53(9), 3066–3077 (2014)
Esposito, G., et al.: Class. Quantum Gravity 24, 6255 (2007)
Ferreira, P.G., Joyce, M.: Phys. Rev. Lett. 79, 4740 (1997)
Ferreira, P.G., Joyce, M.: Phys. Rev. D 58, 023503 (1998)
Folomeev, V.N., Gurovich, V.T.: Gen. Relativ. Gravit. 32(7), 1255 (2000)
Fomin, P.I., et al.: Preprint (2005). gr-qc/0509042
Goswami, G.K., et al.: Mod. Phys. Lett. A 35, 2050086 (2020). https://doi.org/10.1142/S0217732320500868
Halliwell, J.: Phys. Lett. B 185, 341 (1985)
Jamil, M., Debnath, U.: Int. J. Theor. Phys. 50, 1602 (2011)
Kalligas, D., et al.: Gen. Relativ. Gravit. 24, 351 (1992)
Knop, R.A., et al.: Astrophys. J. 598, 102 (2003)
Kumar, S., Singh, C.P.: Astrophys. Space Sci. 312, 57 (2007)
Liddle, A.R., Sharrer, R.J.: Phys. Rev. D 59, 023509 (1998)
Lima, J.A.S., Carvalho, J.C.: Gen. Relativ. Gravit. 26, 909 (1994)
Lima, J.A.S., Maia, J.M.F.: Phys. Rev. D 49, 5597 (1994)
Lima, J.A.S., Trodden, M.: Phys. Rev. D 53, 4280 (1996)
Lucchin, F., Matarrese, S.: Phys. Rev. D 32, 1316 (1985)
Martinez-Gonzalez, E., Sanz, J.L.: Astron. Astrophys. 300, 346 (1995)
Mukhopadhyay, U., et al.: Int. J. Theor. Phys. 50, 752 (2011)
Overduin, J.M., Cooperstock, F.I.: Phys. Rev. D 58, 043506 (1998)
Pavon, D.: Phys. Rev. D 43, 375 (1991)
Pradhan, A.: Int. J. Mod. Phys. D 12, 941 (2003)
Pradhan, A.: Fizika B 16, 205 (2007)
Pradhan, A.: Commun. Theor. Phys. 51, 367 (2009)
Pradhan, A., Kumar, A.: Int. J. Mod. Phys. D 10, 291 (2001)
Pradhan, A., Pandey, A.P.: Int. J. Mod. Phys. D 12, 1299 (2003)
Pradhan, A., Pandey, A.P.: Astrophys. Space Sci. 301, 127 (2006)
Pradhan, A., et al.: Int. J. Theor. Phys. 46, 2774 (2007a)
Pradhan, A., et al.: Rom. J. Phys. 52, 445 (2007b)
Pradhan, A., et al.: Braz. J. Phys. 38, 167 (2008)
Pradhan, A., et al.: Int. J. Theor. Phys. 50, 2923 (2011)
Pradhan, A., et al.: Astrophys. Space Sci. 337, 401 (2012)
Pradhan, A., et al.: Indian J. Phys. 89(5), 503 (2015)
Rahman, M.A., Ansary, M.: Prespace Time J. 4, 871 (2013)
Ray, S., et al.: Int. J. Theor. Phys. 50, 939 (2011)
Riess, A.G., et al.: Astrophys. J. 607, 665 (2004)
Saha, B.: Astrophys. Space Sci. 302, 83 (2006)
Shahalam, M., et al.: Eur. Phys. J. C 75, 395 (2015)
Shen, M.: Int. J. Theor. Phys. 52, 178 (2013)
Silveira, V., Waga, I.: Phys. Rev. D 56, 4625 (1997)
Singh, T., et al.: Gen. Relativ. Gravit. 30, 573 (1998)
Singh, J.P., et al.: Astrophys. Space Sci. 314, 83 (2008)
Singh, M.K., et al.: Int. J. Phys. 1, 77 (2013)
Socorro, J., et al.: Rev. Mex. Fis. 56(2), 166–171 (2010)
Socorro, J., et al.: Adv. High Energy Phys. 2014, 805164 (2014)
Socorro, J., et al.: Astrophys. Space Sci. 360, 20 (2015)
Sola, J., Stefancic, H.: Phys. Lett. B 624, 147 (2005)
Sola, J., Stefancic, H.: Mod. Phys. Lett. A 21, 479 (2006)
Spergel, D.N., et al.: Astrophys. J. Suppl. 170, 377 (2007)
Starobinsky, A.A.: JETP Lett. 8, 757 (1998)
Tegmark, M., et al.: Phys. Rev. D 69, 103501 (2004)
Tripathy, S.K.: Int. J. Theor. Phys. 52, 4218 (2013)
Tripathy, S.K., et al.: Astrophys. Space Sci. 340, 211 (2012)
Vishwakarma, R.G.: Class. Quantum Gravity 17, 3833 (2000)
Vishwakarma, R.G.: Gen. Relativ. Gravit. 33, 1973 (2001)
Wand, D., et al.: Ann. N.Y. Acad. Sci. 688, 647 (1993)
Weetterich, C.: Nucl. Phys. B 302, 668 (1998)
Zia, R., et al.: New Astron. 72, 83 (2019)
Acknowledgements
This work was partially supported by PROMEP grants UGTO-CA-3. S.P.P. and J.S. were partially supported SNI-CONACYT. This work is part of the collaboration within the Instituto Avanzado de Cosmología and Red PROMEP: Gravitation and Mathematical Physics under project Quantum aspects of gravity in cosmological models, phenomenology and geometry of space-time. Many calculations where done by Symbolic Program REDUCE 3.8.
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.
Rights and permissions
About this article
Cite this article
Socorro, J., Pérez-Payán, S., Espinoza-García, A. et al. Cosmological volume acceleration in dust epoch: using scaling solutions and variable cosmological term \(\Lambda (t)\) within an anisotropic cosmological model. Astrophys Space Sci 365, 93 (2020). https://doi.org/10.1007/s10509-020-03810-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-020-03810-9