Exploring Bianchi Type III Universe with Quadratic Trace of Stress-Energy Tensor in f(R, T) Theory of Gravity
Abstract
In this work, we consider a spatially homogeneous and anisotropic Bianchi type III universe in f(R, T) gravity with the functional form f(R, T) = f1(R) + f2(T) with f1(R) = λ1R and f2(T) = λ2T + λ3T2, where λ1, λ2 and λ3 are free parameters. We obtain exact solutions of the gravitational field equations by considering a power-law expansion of a directional scale factor. By keeping a check on the current values of the parameters of cosmological significance such as the Hubble parameter H and the deceleration parameter q, the dynamics and physical characteristics of the model are investigated. We also determine the functional form f(R, T) of our model by evaluating the Ricci scalar R and the trace T of the stress-energy tensor. We find that our model remains anisotropic throughout its evolution and the pressure of the cosmic matter remains negative. The equation of state parameter ω is found to lie in the quintessence regime and therefore our model behaves like quintessence model of dark energy.
Downloads
References
S. Perlmutter, G. Aldering, G. Goldhaber, et al. ”Measurements of Ω and Λ from 42 high-redshift supernovae,” Astrophys. ApJ, 517, (565) (1999). https://doi.org/10.1086/307221
A. G. Riess, A. V. Filippenko, P. Challis, et al. ”Observational evidence from supernovae for an accelerating universe and a cosmological constant,” The Astronomical Journal, 116 (1009) (1998). https://doi.org/10.1086/300499
R. R. Caldwell, M. Doran, ”Cosmic microwave background and supernova constraints on quintessence: Concordance regions and target models,” Phys. Rev. D, 69, 103517 (2004). https://doi.org/10.1103/PhysRevD.69.103517
Zhuo-Yi Huang, B. Wang, E. Abdalla, R.−K, Su, ”Holographic explanation of wide-angle power correlation suppression in the Cosmic Microwave Background Radiation,” J. Cosmol. Astropart. Phys. 5, (013) (2006). https://doi.org/10.1088/1475-7516/2006/05/013
K. Land and J. Magueijo, ”Examination of Evidence for a preferred Axis in the Cosmic Radiation Anisotropy,” Phys. Rev. Lett. 95, 071301 (2005). https://doi.org/10.1103/PhysRevLett.95.071301
C. L. Bennett, M. Halpern, G. Hinshaw, et al. ”First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Preliminary Maps and Basic Results,” Astrophys. J. Suppl. 148, (1) (2003). https://doi.org/10.1086/377253
C. L. Bennett, D. Larson, J. L. Weiland, et al. ”Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results,” ApJS, 208, 20 (2013). https://doi.org/10.1088/0067-0049/208/2/20
D. N. Spergel, L. Verde, H. V. Peiris, et al. ”First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: determination of cosmological parameters,” ApJS, 148, (175) (2003). https://doi.org/10.1086/377226
D. N. Spergel, R. Bean, O. Dor’e, et al. ”Three-yearWilkinson Microwave Anisotropy Probe (WMAP) observations: implications for cosmology,” ApJS, 170, 377 (2007). https://doi.org/10.1086/513700
M. Tegmark, M. A. Strauss, M. R. Blanton, et al. ”Cosmological parameters from SDSS and WMAP,” Phys. Rev. D, 69, 103501 (2004). https://doi.org/10.1103/PhysRevD.69.103501
L. Anderson, E. Aubourg, S. Bailey, D. Bizyaev, M. Blanton, A. S. Bolton, et al. ”The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Release 9 spectroscopic galaxy sample,” Monthly Notices of the Royal Astronomical Society, 427(4), 3435-3467 (2012). https://doi.org/10.1093/mnras/stu523
C. Blake, E. A. Kazin, F. Beutler, T. M. Davis, D. Parkinson, S. Brough, et al. ”The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations,” Monthly Notices of the Royal Astronomical Society, 418(3), 1707-1724 (2011). https://doi.org/10.1111/j.1365-2966.2011.19592.x
N. Padmanabhan, X. Xu, D. J. Eisenstein, R. Scalzo, A. J. Cuesta, K. T. Mehta, E. Kazin, ”A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillations-I. Methods and application to the Sloan Digital Sky Survey,” Monthly Notices of the Royal Astronomical Society, 427(3), 2132-2145 (2012). https://doi.org/10.1111/j.1365-2966.2012.21888.x
T. Barreiro, E. J. Copeland and N. J. Nunes, ”Quintessence arising from exponential potentials,” Phys. Rev. D. 61, 127301 (2000). https://doi.org/10.1103/PhysRevD.61.127301
T. Chiba, T. Okabe, M. Yamaguchi, ”Kinetically driven quintessence,” Phys. Rev. D, 62, 023511 (2000). https://doi.org/10.1103/PhysRevD.62.023511
T. Padmanabhan, ”Accelerated expansion of the universe driven by tachyonic matter,”Phys. Rev. D, 66, 021301 (2002). https://doi.org/10.1103/PhysRevD.66.021301
R. R. Caldwell, M. Kamionkowski and N. N.Weinberg, ”Phantom Energy: Dark Energy with ω <-1 Causes a Cosmic Doomsday,” Phys. Rev. Lett. 91, 071301 (2003). https://doi.org/10.1103/PhysRevLett.91.071301
M. Li, ”A model of holographic dark energy,”Phys. Lett. B, 603, 1 (2004), https://doi.org/10.1016/j.physletb.2004.10.014
C. Tsallis, and L. J. L. Cirto, ”Black hole thermodynamical entropy,” Eur. Phys. J. C, 73, 2487 (2013), https://doi.org/10.1140/epjc/s10052-013-2487-6
D. J. Barrow, ”The area of a rough black hole,” Phys. Lett. B, 808, 135643 (2020). https://doi.org/10.1016/j.physletb.2020.135643
A. Kamenshchik, U. Moschella, V. Pasquier, ”An alternative to quintessence,” Phys. Lett. B, 511, 265-268 (2001). https://doi.org/10.1016/S0370-2693(01)00571-8
M. C. Bento, O. Bertolami, and A. A. Sen, ”Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter unification,” Phys. Rev. D, 66, 043507 (2002). https://doi.org/10.1103/PhysRevD.66.043507
H. B. Benaoum, ”Modified Chaplygin Gas Cosmology,” Advances in High Energy Physics, 2012, 357802 (2012). https://doi.org/10.1155/2012/357802
S. M. Carroll, V. Duvvuri, M. Trodden, and M. S. Turner, ”Is cosmic speed-up due to new gravitational physics?” Phys. Rev. D, 70, 043528 (2004). https://doi.org/10.1103/PhysRevD.70.043528
T. Harko, F. S. N. Lobo, S. Nojiri and S. D. Odintsov, ”f(R, T) gravity,” Phys. Rev. D, 84, 024020 (2011). https://doi.org/10.1103/PhysRevD.84.024020
S. M. Carroll, A. D. Felice, V. Duvvuri, D. A. Easson, M. Trodden, and M. S. Turner, ”Cosmology of generalized modified gravity models,” Phys. Rev. D, 71, 063513 (2005). https://doi.org/10.1103/PhysRevD.71.063513
R. Ferraro, and F. Fiorini, ”Modified teleparallel gravity: Inflation without an inflaton,” Phys. Rev. D, 75, 084031 (2007). https://doi.org/10.1103/PhysRevD.75.084031
J. B. Jim´enez, L. Heisenberg, and T. Koivisto, ”Coincident general relativity,” Phys. Rev. D, 98(4), 044048 (2018). https://doi.org/10.1103/PhysRevD.98.044048
M.J.S. Houndjo, ”Reconstruction of f(R, T) gravity describing matter dominated and accelerated phases,” Int. J. Mod. Phys. D, 21, 1250003-1250016 (2012). https://doi.org/10.1142/S0218271812500034
P. K. Sahoo, S. K. Sahu, and A. Nath, ”Anisotropic Bianchi-III cosmological model in f(R, T) gravity,” Eur. Phys. J. Plus, 131, 18 (2016). https://doi.org/10.1140/epjp/i2016-16018-6
G. C. Samanta, and B. K. Bishi, ”Geometry of the Universe Described by Wet Dark Fluid in f(R, T) Theory of Gravity,” Iran. J. Sci. Technol. Trans. A Sci. 41, 223 (2017). https://doi.org/10.1007/s40995-017-0215-z
S. Arora, S. Bhattacharjee, and P. K. Sahoo, ”Late-time viscous cosmology in f(R, T) gravity,” New Astronomy, 82, 101452 (2021). https://doi.org/10.1016/j.newast.2020.101452
C. R. Mahanta, S. Deka, and K. Pathak, ”Anisotropic Cosmological Model in f(R, T) Theory of Gravity with a Quadratic Function of T,” East European Journal of Physics, (3), 43-52 (2023). https://doi.org/10.26565/2312-4334-2023-3-02
C. R. Mahanta, K. Pathak, and D. Das, ”FLRW Cosmological Model with Quadratic Functional Form in f(R, T) Theory of Gravity,” East European Journal of Physics, (1), 29-43 (2025). https://doi.org/10.26565/2312-4334-2025-1-03
M. K. Verma, M. K. Singh, and S. Ram, ”Anisotropic Bulk Viscous Fluid Cosmological Model with Zero-Rest-Mass Scalar Field and Time-Dependent Cosmological Term,” Int. J. Theor. Phys. 51, 1729-1736 (2012). https://doi.org/10.1007/s10773-011-1050-1
D. R. K. Reddy, R. Santikumar, and R. L. Naidu, ”Bianchi type-III cosmological model in f(R, T) theory of gravity,” Astrophys. Space Sci. 342, 249-252 (2012). https://doi.org/10.1007/s10509-012-1158-7
V. Sahni, et al., ”Statefinder - a new geometrical diagnostic of dark energy,” JETP Lett. 77, 201 (2003). https://doi.org/10.1134/1.1574831
Copyright (c) 2026 Chandra Rekha Mahanta, Kankana Pathak
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
