Exploring plane symmetric space-time in f(R) modified gravitational theory
Abstract
This paper investigates a plane-symmetric cosmological model (PSCM) in the context of modified f(R) gravity theory, incorporating both vacuum and non-vacuum scenarios. A perfect fluid is assumed as the matter source. To obtain the solutions, we consider the premise of constant scalar curvature. By applying the conservation law for Einstein's field equation, Tij;j, and the power-law assumption, we retrieve some well-known solutions. We solved the field equations by making a specific assumption that involved a transformation A2B=U . This study explores the physical and kinematic characteristics of specific cosmological models, along with an examination of the statefinder diagnostic—a key tool for analysing the universe’s evolutionary trajectory. The work provides important insights into the behaviour of anisotropic models within the context of modified f(R) gravity. It highlights the interplay between matter distribution and spacetime geometry, particularly emphasizing how assuming a constant scalar curvature aids in simplifying and solving the corresponding field equations. The resulting solutions enhance our understanding of cosmic evolution governed by modified f(R) gravity.
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References
H.A. Buchdahl, “Non-linear Lagrangians and Cosmological Theory”. Mon. Not. R. Astro. Soc., 150, 1-8 (1970). https://doi.org/10.1093/mnras/150.1.1
O. Bertolami, FG. Pedro, and M.L. Delliou, “Dark energy-dark matter interaction and putative violation of the equivalence principle from the Abell cluster A586,” Phys. Letters B, 654, 165-169 (2007). https://doi.org/10.1016/j.physletb.2007.08.046
Carroll, et al., “Is cosmic speed-up due to new gravitational physics?” Phys. Rev. D, 70, 043528 (2004). https://doi.org/10.1103/PhysRevD.70.043528
C.L. Bennet, et al., Astrophys. J. Suppl. “First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Preliminary Maps and Basic Results,” 148, 1(2003). https://doi.org/10.1086/377253; Spergel, et al., “First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Determination of Cosmological Parameters,” Astrophys. J. Suppl. 148, 175(2003). https://doi.org/10.1086/377226
Riess, et al. (Supernovae Search Team), Astron. J. “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,” 116, 1009 (1998). https://doi.org/10.1086/300499; Astrophys. J. “Type Ia Supernova Discoveries at z > 1 from the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution,” 607, 665 (2004). https://doi.org/10.1086/383612; Perlmutter, S., et al., Astrophys. J. “Measurements of Ω and Λ from 42 High-Redshift Supernovae,” 517, 565 (1999). https://doi.org/10.1086/307221; Astier, P., et al., “The Supernova Legacy Survey: measurement of ΩΜ, ΩΛ and w from the first year data set,” Astron. Astrophys. 447, 31-48 (2006). https://doi.org/10.1051/0004-6361:20054185
S.W. Allen, et al., “Constrains on dark energy from Chandra observations of the largest relaxed galaxy clusters,” Mon. Not. R. Astron. Soc. 353, 457-467 (2004). https://doi.org/10.1111/j.1365-2966.2004.08080.x
N. Tegmark, et al., “Cosmological parameters from SDSS and WMAP,” Phys. Rev. D, 69, 103501 (2004). https://doi.org/10.1103/PhysRevD.69.103501
S. Perlmutter, “Cosmology from Type Ia Supernovae,” Bulletin of the American Astronomical Society, 29, 1351, (1997). https://arxiv.org/pdf/astro-ph/9812473
K. Bamba, S. Capozziello, S. Nojiri, and S.D. Odintsov, “Dark Energy Cosmology: The Equivalent Description via Different Theoretical Models and Cosmography Tests,” Astrophys. And Space Sci. 342, 155-228 (2012). https://doi.org/10.1007/s10509-012-1181-8
S. Nojiri, and S.D. Odintsov, “Unified Cosmic History in Modified Gravity: from f(R) Theory to Lorentz Non-Invarient Models,” Phys. Report, 505, 59-144 (2011). https://doi.org/10.1016/j.physrep.2011.04.001
B. Mishra, and S.K. Tripathy, “Anisotropic Dark Energy Model with a Hybrid Scale Factor,” Modern Phys. Letters A, 30, 1550175 (2015). https://doi.org/10.1142/S0217732315501758
F.M.D. Esmaeili, “Dynamics of Bianchi I Universe in Extended Gravity with Scale Factor,” Journal of High Energy Physics, Gravitation and Cosmology, 4, 716-730 (2018). https://doi.org/10.4236/jhepgc.2018.44040
M.F. Shamir, “Exploring Plane-Symmetric Solutions in f(R) Gravity,” Journal of Experimental and Theoretical Physics, 122, 331-337 (2016). https://doi.org/10.1134/S106377611601009X
V.B. Raut, et al., “Plane Symmetric Vacuum Cosmological Model with a special form of Deceleration Parameter in f(R) Theory of Gravity,” Physical Science International Journal, 5(1), 74-80 (2015). https://doi.org/10.9734/PSIJ/2015/13999
A.S. Agrawal, et al., “Gravitational baryogenesis model’s comparison in f(R) gravity,” Chinese journal of physics, 71, 333-340 (2021). https://doi.org/10.1016/j.cjph.2021.03.004
K.P. Singh, J. Baro, A.J. Meitei, “Higher Dimensional Bianchi Type-I Cosmological Model with Massive String in General Relativity,” Front. Astron. Space Sci. 8, 777554 (2021). https://doi.org/10.3389/fspas.2021.777554
A.S. Agrawal, S. Zerbini, and B. Mishra, “Black Holes and Wormholes Beyond Classical General Relativity,” arXiv:2406.01241[gr-qc], (2024). https://doi.org/10.48550/arXiv.2406.01241
M.R. Karim, “Bianchi Type-I Anisotropic Universe with Meric Potential in Saez-Ballester Theory of Gravitation,” Journal of Applied Mathematics and Physics, 10, 3072-3082 (2022). https://doi.org/10.4236/jamp.2022.1010205
A.M. Al-Haysah, and A.H. Hasmani, “Higher dimensional Bianchi type-I string cosmological model in f(R) theory of gravity,” Heliyon, 7, e08063 (2021). https://doi.org/10.1016/j.heliyon.2021.e08063
L.S. Ladke, and R.D. Mishra, “Higher Dimensional Plane Symmetric Solutions in f(R) Theory of Gravitation,” Prespacetime journal, 8(5), 542-554 (2017). https://prespacetime.com/index.php/pst/article/download/1259/1228
L.S. Ladke, R.D. Mishra, and S.R. Gomkar, “Static Interior Plane Symmetric five-dimensional solutions in f(R) gravity,” International Journal of Mathematical Archive, 9(4), 151-162 (2018).
V.A. Thakare, R.V. Mapari, and S.S. Thakre, “Five- Dimensional Plane Symmetric Cosmological Model with Quadratic Equation of State in f (R, T) Theory of Gravity,” East Eur. J. Phys. (3), 108-121 (2023). https://doi.org/10.26565/2312-4334-2023-3-08
U.K. Sharma, R. Zia, A. Pradhan, and A. Beesham, “Stability of LRS Bianchi type-I cosmological models in f (R, T)-gravity,” Research in Astronomy and Astrophysics, 19(4), 55-68 (2019). https://doi.org/10.1088/1674–4527/19/4/55
A. Dabre, and P. Makode, “Viscous Plane Symmetric String Cosmological Model in f(R) Gravity,” Astrophysics, 67, 161-177 (2024). https://doi.org/10.1007/s10511-024-09826-1
D.D. Pawar, and A.G. Deshmukh, “Bulk Viscous Fluid Plane Symmetric String Cosmological Model in General Relativity,” Bulg. J. Phys. 37, 56-63 (2010). https://www.bjp-bg.com/papers/bjp2010_1_56-63.pdf
A. Cassado-Turrion, A. de la Cruz-Dombriz, and A. Dobado, “Physical nonviability of a wide class of f(R) models and their constant-curvature solutions,”. Phys. Rev. D, 108, 064006 (2023). https://doi.org/10.1103/PhysRevD.108.064006
A. Larranaga, “A rotating charged black hole solution in f(R) gravity,” Pramana journal of physics, 78(5), 697-703 (2012). https://doi.org/10.1007/s12043-012-0278-5
M. Calza, M. Rinaldi, and L. Sebastiani, “A special class of solutions in F(R)- gravity,” Eur. Phys. J. C, 78, 178 (2018). https://doi.org/10.1140/epjc/s10052-018-5681-8
M. Sharif, and M.F. Shamir, “Non-Vacuum Bianchi Types I and V in f(R) Gravity,” Gen. Rel. Grav. 42, 2643-2655 (2010). https://doi.org/10.1007/s10714-010-1005-5
M. Sharif, and M.F. Shamir, “Plane Symmetric Solutions in f(R) Gravity,” Mod. Phys. Lett. A, 25, 1281-1288 (2010). https://doi.org/10.1142/S0217732310032536
D.R.K. Reddy, K.S. Adhav, and S.L. Munde, “Vacuum Solutions of Bianchi Type-I and V Models in f(R) Gravity with a Special Form of Deceleration Parameter,” Int. J. Sci. Adv. Tech. 4, (2014).
A.D. Linde, “Inflationary Cosmology,” in: Inflationary Cosmology. Lecture Notes in Physics, edited by M. Lemoine, J. Martin, and P. Peter, 738, (Springer, Berlin, Heidelberg), (2008), pp. 1-54. https://doi.org/10.1007/978-3-540-74353-8_1
P.A.R. Ade, (Planck Collaboration), “Plank 2013 results. XVI. Cosmological Parameters,” Astron. Astrophys. 571, A16, (2014). https://doi.org/10.1051/0004-6361/201321591
R.K. Tiwari, R. Singh, and B.K. Shukla, “A Cosmological Model with Variable Deceleration parameter,” The African Review of Physics, 10, 395-402 (2015). http://aphysrev.ictp.it/index.php/aphysrev/article/download/1137/460
P.K. Ray, and R.R. Baruah, “Anisotropic cloud string cosmological model with five-dimensional Kaluza Klein space-time,” Frontiers in Astronomy and Space Sciences, 9, 869020 (2022). https://doi.org/10.3389/fspas.2022.869020
V. Sahni, T.D. Saini, A.A. Starobinsky, and U. Alam, “Statefinder – A new geometrical diagnostic of dark energy,” J. Exp. Theor. Phys. Lett. 77, 201-206 (2003). https://doi.org/10.1134/1.1574831
U. Alam, V. Sahni, T.D. Saini, and A.A. Starobinsky, “Exploring the Expanding Universe and Dark Energy using the Statefinder Diagnostic,” Mon. Not. R. Astron. Soc. 344, 1057 (2003). https://doi.org/10.1046/j.1365-8711.2003.06871.x
S. Appleby, R. Battye, and A. Starobinsky, “Curing singularities in cosmological evolution of f(R) gravity,” JCAP, 1006, 005 (2010). https://doi.org/10.1088/1475-7516/2010/06/005
F. Yu, J.L. Cui, J.F. Zhang, and X. Zhang, “Statefinder hierarchy exploration of the extended Ricci dark energy,”. Eur. Phys. J. C, 75, 274 (2015). https://doi.org/10.1140/epjc/s10052-015-3505-7
M.Z. Khurshudyan, and A.N. Makarenko, “On a phenomenology of the accelerated expansion with a varying ghost dark energy,” Astrophys. Space Sci. 361, 187 (2016). https://doi.org/10.1007/s10509-016-2775-3
B.K. Shukla, R.K. Tiwari, D. Sofuoglu, and A. Beesham, “Quintessence’s Universe in f(R, Lm) gravity with special form of deceleration parameter,” (2023). https://doi.org/10.48550/arXiv.2306.09387
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