FLRW Cosmological Model with Quadratic Functional Form in f(R, T) Theory of Gravity
Abstract
This work investigates a spatially homogeneous and isotropic flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe within the context of f(R, T) gravity as introduced by Harko et al., [Phys. Rev. D, 84, 024020 (2011)]. The present work deals with the functional form f(R, T) = f1(R) + f2(T) with f1(R) = R + λ1R2 and f2(T) = 2λ2T where λ1 and λ2 are arbitrary constants, R and T being the Ricci scalar and the trace of the stress-energy tensor Tij respectively. We present a novel cosmological model in the framework of f(R, T) gravity, exploring the dynamics of the FLRW universe through an exact solution to the gravitational field equations. By employing an innovative ansatz for the Hubble parameter, H = α (1 + 1/t) where α is a positive constant, we capture a evolutionary history of the universe. This approach provides a natural pathway to investigate key cosmological parameters, such as the scale factor, deceleration parameter, jerk, snap, lerk parameters and energy conditions, revealing intriguing insights into the universe’s expansion dynamics. We also discuss the statefinder diagnostic. Our results offer a deeper understanding of cosmic evolution within the f(R, T) gravity framework.
Downloads
References
Riess, A. G., Filippenko, A. V., Challis, P. et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116, 1009 (1998), https://doi.org/10.1086/300499
Perlmutter, S., Aldering, G., Valle, M. D., Deustua, S., Ellis, R. S., Fabbro, S., Fruchter, A. et al., Discovery of a supernova explosion at half the age of the Universe, Nature 391, 51 (1998), https://doi.org/10.1038/34124
Perlmutter, S., Aldering, G., Goldhaber, G. et al., Measurements of Ω and Λ from 42 high-redshift supernovae, Astrophys. J. 517, 565 (1999), https://doi.org/10.1086/307221
Bennett, C. L., Halpern, M., Hinshaw, G. et al., First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Preliminary Maps and Basic Results, Astrophys. J. Suppl. Ser. 148, 1 (2003), https://doi.org/10.1086/377253
Bennett, C. L., Larson, D.,Weiland, J. L. et al., Nine-YearWilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, Astrophys. J. Suppl. Ser. 208, 20 (2013), https://doi.org/10.1088/0067-0049/208/2/20
Spergel, D. N., Verde, L., Peiris, H. V. et al., First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: determination of cosmological parameters, Astrophys. J. Suppl. Ser. 148, 175 (2003), https://doi.org/10.1086/377226
Spergel, D. N., Bean, R., Doré, O. et al., Three-yearWilkinson Microwave Anisotropy Probe (WMAP) observations: implications for cosmology, Astrophys. J. Suppl. Ser. 170, 377 (2007), https://doi.org/10.1086/513700
Hinshaw, G. et al., Nine year wilkinson microwave anisotropy probe observations: cosmological parameter results, Astrophys. J. Suppl. Ser. 208, 19 (2013), https://doi.org/10.1088/0067-0049/208/2/19
Tegmark, M., Strauss, M. A., Blanton, M. R. et al., Cosmological parameters from SDSS and WMAP, Phys. Rev. D 69, 103501 (2004), https://doi.org/10.1103/PhysRevD.69.103501
Caldwell, R. R., Doran, M., 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
Huang, Z.−Y., Wang, B., Abdalla, E., Su, R.−K., Holographic explanation of wide-angle power correlation suppression in the Cosmic Microwave Background Radiation, J. Cosmo. Astropart. Phys. 5, 013 (2006), https://doi.org/10.1088/1475-7516/2006/05/013
Zwicky, F., The redshift of extragalactic nebulae, Helvetica Physica Acta, 6, 110 (1933), https://doi.org/10.48550/arxiv.1711.01693
Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S., Is cosmic speed-up due to new gravitational physics ?, Phys. Rev. D 70, 043528 (2004), https://doi.org/10.1103/PhysRevD.70.043528
Harko, T., Lobo, F. S. N., Nojiri, S., Odintsov, S. D., f(R, T) gravity, Phys. Rev. D 84, 024020 (2011), https://doi.org/10.1103/PhysRevD.84.024020
Brans, C., Dicke, R. H., Mach’s Principle and a Relativistic Theory of Gravitation, Phys. Rev. D 124, 925 (1961), https://doi.org/10.1103/PhysRev.124.925
Ferraro, R., Fiorini, F., Modified teleparallel gravity: Inflation without an inflaton, Phys. Rev. D 75, 084031 (2007), https://doi.org/10.1103/PhysRevD.75.084031
Carroll, S.M., Felice, A.D., Duvvuri, V., Easson, D.A., Trodden, M., Turner, M.S., Cosmology of generalized modified gravity models, Phys. Rev. D 71, 063513 (2005), https://doi.org/10.1103/PhysRevD.71.063513
Jiménez, J. B., Heisenberg, L., Koivisto, T., Coincident general relativity, Phys. Rev. D 98, 044048 (2018), https://doi.org/10.1103/PhysRevD.98.044048
Bamba, K. et al., Finite-time future singularities in modified Gauss-Bonnet and F(R,G) gravity and singularity avoidance, Eur. Phys. J. C 67, 295 (2010), https://doi.org/10.1140/epjc/s10052-010-1292-8
Xu, Y., Li, G., Harko, T., Liang, S., f(Q, T) gravity, Eur. Phys. J. C 79, 708 (2019), https://doi.org/10.1140/epjc/s10052-019-7207-4
Houndjo, M. J. S., Reconstruction of f(R, T) gravity describing matter dominated and accelerated phases, Int. J. Mod. Phys. D, 21, 1250003 (2012), https://doi.org/10.1142/S0218271812500034
Bhattacharjeea, S. and Sahoo, P. K., Redshift Drift in f(R, T) Gravity, New Astron. 81, 101425 (2020), https://doi.org/10.1016/j.newast.2020.101425
Pradhan, A., Goswami, G., Rani R., Beesham, A., An f(R, T) gravity based FLRWmodel and observational constraints, Astronomy and Computing 44, 100737 (2023), https://doi.org/10.1016/j.ascom.2023.100737
Starobinsky, A. A., A new type of isotropic cosmological models without singularity, Phys. Lett. B 91, 99 (1980), https://doi.org/10.1016/0370-2693(80)90670-X
Zubair, M., Noureen, I., Evolution of axially symmetric anisotropic sources in f(R, T) gravity, Eur. Phys. J. C 75, 265 (2015), https://doi.org/10.1140/epjc/s10052-015-3496-4
Zubair, M., Noureen, I., Bhatti, A.A., Abbas, G., Shear-free condition and dynamical instability in f(R, T) gravity, Eur. Phys. J. C 75, 323 (2015), https://doi.org/10.1140/epjc/s10052-015-3547-x
Sahoo, P.K., Moraes, P. H. R. S., Sahoo, P.,Wormholes in R2-gravity within the f(R, T) formalism, Eur. Phys. J. C 78, 46 (2018), https://doi.org/10.1140/epjc/s10052-018-5538-1
Sahoo, P.K., Moraes, P. H. R. S., Sahoo, P., Bishi, B. K., f(R, T) = f(R) + λT gravity models as alternatives to cosmic acceleration, Eur. Phys. J. C 78, 736 (2018), https://doi.org/10.1140/epjc/s10052-018-6211-4
Vinutha, T., Kavya, K. S., Bianchi type cosmological models in f(R, T) theory with quadratic functional form, Eur. Phys. J. Plus 135, 306 (2020), https://doi.org/10.1140/epjp/s13360-020-00309-8
Bishi, B. K. et al., Domain Walls and Quark Matter Cosmological Models in f(R, T) = R + aR2 + kT gravity, Iran. J. Sci. Technol. Trans. Sci. 45, 1835 (2021), https://doi.org/10.1007/s40995-021-01113-4
Hassan, A. et al., An Interacting Two-Fluid Scenario for Dark Energy in an FRW Universe, Chinese Phys. Lett. 28, 039801 (2011), https://doi.org/10.1088/0256-307X/28/3/039801
Sahni, V. et al., Statefinder - a new geometrical diagnostic of dark energy, JETP Lett. 77, 201 (2003), https://doi.org/10.1134/1.1574831
Copyright (c) 2025 Chandra Rekha Mahanta, Kankana Pathak, Dibyajyoti Das
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).
