A Study of Evolution of Cosmological Parameters Based on a Dark Energy Model in the Framework of Brans-Dicke Gravity

Keywords: Brans-Dicke gravity, Dark Energy, Gravitational constant, Cosmological constant, Cosmographic analysis, Om diagnostic, Statefinder diagnostic


The objective of the present study is to find the characteristics of evolution of a homogeneous and isotropic universe in the framework of Brans-Dicke (BD) theory of gravity. FLRW space-time, with zero spatial curvature, has been used to obtain BD field equations. Scale factor and Hubble parameter have been obtained from an ansatz for the deceleration parameter, assumed on the basis of its property of signature flip indicating a change of phase from deceleration to acceleration. Validation of the model has been achieved by a suitable parametrization of that ansatz. Expressions for energy density, pressure, equation of state (EoS) parameter, cosmological constant, gravitational constant have been derived and depicted graphically. The gravitational constant is found to decrease with time at a gradually decreasing rate. The Hubble parameter, deceleration parameter and energy density decrease with time, which is in agreement with many other studies. The value of the EoS parameter at the present epoch is negative, and it becomes more negative with time. The cosmological constant increases very rapidly in the early universe from negative to smaller negative values, becoming positive finally, with a much slower change thereafter. A cosmographic and a geometrical analysis have been carried out. It is observed that a gradual transition takes place from a regime of quintessence to phantom dark energy. An important finding of this study is that the signature flip of the deceleration parameter takes place almost simultaneously with the signature flip of the cosmological constant, implying a connection between accelerated expansion and dark energy, which is represented here by the cosmological constant. Unlike the common practice of using arbitrary units, proper SI units for all measurable quantities have been used. This theoretical investigation provides the reader with a simple method to formulate models in the framework of BD theory.


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S. Perlmutter, G. Aldering, M. D. Valle, S. Deustua, R. S. Ellis, S. Fabbro, A. Fruchter, G. Goldhaber, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, R. A. Knop, C. Lidman, R. G. McMahon, P. Nugent, R. Pain, N. Panagia, C. R. Pennypacker, P. Ruiz-Lapuente, B. Schaefer, and N. Walton, “Discovery of a supernova explosion at half the age of the Universe,” Nature, 391(6662), 51–54 (1998). https://doi.org/10.1038/34124

A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, and J. Tonry, "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant," Astron. J. 116(3), 1009–1038 (1998). https://doi.org/10.1086/300499

M. Kowalski, D. Rubin, G. Aldering, R. J. Agostinho, A. Amadon, R. Amanullah, C. Balland, K. Barbary, G. Blanc, P. J. Challis, A. Conley, N. V. Connolly, R. Covarrubias, K. S. Dawson, S. E. Deustua, R. Ellis, S. Fabbro, V. Fadeyev, X. Fan, B. Farris, G. Folatelli, B. L. Frye, G. Garavini, E. L. Gates, L. Germany, G. Goldhaber, B. Goldman, A. Goobar, D. E. Groom, J. Haissinski, D. Hardin, I. Hook, S. Kent, A. G. Kim, R. A. Knop, C. Lidman, E. V. Linder, J. Mendez, J. Meyers, G. J. Miller, M. Moniez, A. M. Mourão, H. Newberg, S. Nobili, P. E. Nugent, R. Pain, O. Perdereau, S. Perlmutter, M. M. Phillips, and J. L. Yun, "Improved Cosmological Constraints from New, Old, and Combined Supernova Data Sets," Astrophys. J. 686(2), 749–778 (2008). https://doi.org/10.1086/589937

J. Guy, M. Sullivan, A. Conley, N. Regnault, P. Astier, C. Balland, S. Basa, R. G. Carlberg, D. Fouchez, D. Hardin, I. M. Hook, D. A. Howell, R. Pain, N. Palanque-Delabrouille, K. M. Perrett, C. J. Pritchet, J. Rich, V. Ruhlmann-Kleider, D. Balam, S. Baumont, R. S. Ellis, S. Fabbro, H. K. Fakhouri, N. Fourmanoit, S. González-Gaitán, M. L. Graham, E. Hsiao, T. Kronborg, C. Lidman, A. M. Mourao, S. Perlmutter, P. Ripoche, N. Suzuki, and E. S. Walker, "The Supernova Legacy Survey 3-year sample: Type Ia supernovae photometric distances and cosmological constraints," Astron. & Astrophys. 523, A7 (2010). https://doi.org/10.1051/0004-6361/201014468

S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz‐Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch, and T. S. C. Project, "Measurements of Ω and Λ from 42 High‐Redshift Supernovae," Astrophys. J. 517(2), 565–586 (1999). https://doi.org/10.1086/307221

E. J. Copeland, M. Sami, and S. Tsujikawa, "Dynamics of dark energy," Int. J. Mod. Phys. D 15(11), 1753–1935 (2006). https://doi.org/10.1142/s021827180600942x

G. K. Goswami, A. Pradhan, M. Mishra, and A. Beesham, "FRW dark energy cosmological model with hybrid expansion law," New Astron. 73, 101284 (2019). https://doi.org/10.1016/j.newast.2019.101284

S. K. Tripathy, S. K. Pradhan, Z. Naik, D. Behera, and B. Mishra, "Unified dark fluid and cosmic transit models in Brans–Dicke theory," Phys. Dark Universe 30, 100722 (2020). https://doi.org/10.1016/j.dark.2020.100722

S. K. J. Pacif, "Dark energy models from a parametrization of H: a comprehensive analysis and observational constraints," Eur. Phys. J. Plus 135(10) (2020). https://doi.org/10.1140/epjp/s13360-020-00769-y

C. Brans and R. H. Dicke, "Mach's Principle and a Relativistic Theory of Gravitation," Phys. Rev. 124(3), 925–935 (1961). https://doi.org/10.1103/physrev.124.925

S. Capozziello, S. Carloni and A. Troisi, “Quintessence without scalar fields,” arXiv preprint astro-ph/0303041. 2003 Mar 3. Available from: https://doi.org/10.48550/arXiv.astro-ph/0303041

T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, "f(R,T)gravity," Phys. Rev. D 84(2) (2011). https://doi.org/10.1103/physrevd.84.024020

S. Kalyana Rama and S. Ghosh, "Short distance repulsive gravity as a consequence of non-trivial PPN parameters β and γ," Phys. Lett. B 384(1-4), 50–57 (1996). https://doi.org/10.1016/0370-2693(96)00818-0

O. Bertolami and P. J. Martins, "Nonminimal coupling and quintessence," Phys. Rev. D 61(6) (2000). https://doi.org/10.1103/physrevd.61.064007

N. Banerjee and D. Pavón, "Cosmic acceleration without quintessence," Phys. Rev. D 63(4) (2001). https://doi.org/10.1103/physrevd.63.043504

D. R. K. Reddy and M. V. S. Rao, "Axially Symmetric String Cosmological Model In Brans-Dicke Theory of Gravitation," Astrophys. Space Sci. 305(2), 183–186 (2006). https://doi.org/10.1007/s10509-006-9062-7

R. K. Mishra and A. Chand, "Cosmological models in alternative theory of gravity with bilinear deceleration parameter," Astrophys. Space Sci. 361(8) (2016). https://doi.org/10.1007/s10509-016-2837-6

G. K. Goswami, "Cosmological parameters for spatially flat dust filled Universe in Brans-Dicke theory," Res. Astron. Astrophys. 17(3), 27 (2017). https://doi.org/10.1088/1674-4527/17/3/27

R. K. Mishra and H. Dua, "Evolution of FLRW universe in Brans-Dicke gravity theory," Astrophys. Space Sci. 366(1) (2021). https://doi.org/10.1007/s10509-020-03908-0

C. P. Singh and S. Kaur, "Probing bulk viscous matter-dominated model in Brans-Dicke theory," Astrophys. Space Sci. 365(1) (2019). https://doi.org/10.1007/s10509-019-3713-y

R. Prasad, A. K. Yadav, and A. K. Yadav, "Constraining Bianchi type V universe with recent H(z) and BAO observations in Brans–Dicke theory of gravitation," Eur. Phys. J. Plus 135(3) (2020). https://doi.org/10.1140/epjp/s13360-020-00308-9

S. K. Tripathy, S. K. Pradhan, Z. Naik, D. Behera, and B. Mishra, "Unified dark fluid and cosmic transit models in Brans–Dicke theory," Phys. Dark Universe 30, 100722 (2020). https://doi.org/10.1016/j.dark.2020.100722

M. Visser, “Cosmography: Cosmology without the Einstein equations,” Gen Relativ Gravit 37, 1541–1548 (2005). https://doi.org/10.1007/s10714-005-0134-8

M. Visser, "Jerk, snap and the cosmological equation of state," Class. Quantum Gravity 21(11), 2603–2615 (2004). https://doi.org/10.1088/0264-9381/21/11/006

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(5), 201–206 (2003). https://doi.org/10.1134/1.1574831

V. Sahni, A. Shafieloo, and A. A. Starobinsky, "Two new diagnostics of dark energy," Phys. Rev. D 78(10) (2008). https://doi.org/10.1103/physrevd.78.103502

S. Ray, U. Mukhopadhyay, and S. B. D. Choudhury, "Dark Energy Models with a time-dependent gravitational constant," Int. J. Mod. Phys. D 16(11), 1791–1802 (2007). https://doi.org/10.1142/s0218271807011097

S. Ray, U. Mukhopadhyay, S. Ray, and A. Bhattacharjee, "Dirac's large number hypothesis: A journey from concept to implication," Int. J. Mod. Phys. D 28(08), 1930014 (2019). https://doi.org/10.1142/s0218271819300143

A. Pradhan, G. Goswami, and A. Beesham, "The reconstruction of constant jerk parameter with f(R,T) gravity," J. High Energy Astrophys. 2023. https://doi.org/10.1016/j.jheap.2023.03.001

C. R. Mahanta, S. Deka, and M. P. Das, “Bianchi Type V Universe with Time Varying Cosmological Constant and Quadratic Equation of State in f(R,T) Theory of Gravity,” East Eur. J. Phys. 1, 44-52 (2023). https://doi.org/10.26565/2312-4334-2023-1-04

G. P. Singh, A. Y. Kale, and J. Tripathi, “Dynamic cosmological ‘constant’in brans dicke theory,” Romanian Journal of Physics 58(1-2), 23-35 (2013). https://rjp.nipne.ro/2013_58_1-2/0023_0035.pdf

M. Moksud Alam, "Kaluza-Klein Cosmological Models with Barotropic Fluid Distribution," Phys. & Astron. Int. J. 1(3) (2017). https://doi.org/10.15406/paij.2017.01.00018

G. P. Singh, B. K. Bishi, and P. K. Sahoo, "Scalar field and time varying cosmological constant in f ( R , T ) gravity for Bianchi type-I universe," Chin. J. Phys. 54(2), 244–255 (2016). https://doi.org/10.1016/j.cjph.2016.04.010

R. K. Tiwari, F. Rahaman, and S. Ray, "Five Dimensional Cosmological Models in General Relativity," Int. J. Theor. Phys. 49(10), 2348–2357 (2010). https://doi.org/10.1007/s10773-010-0421-3

M. Tegmark, M. R. Blanton, M. A. Strauss, F. Hoyle, D. Schlegel, R. Scoccimarro, M. S. Vogeley, D. H. Weinberg, I. Zehavi, A. Berlind, T. Budavari, A. Connolly, D. J. Eisenstein, D. Finkbeiner, J. A. Frieman, J. E. Gunn, A. J. S. Hamilton, L. Hui, B. Jain, D. Johnston, S. Kent, H. Lin, R. Nakajima, R. C. Nichol, J. P. Ostriker, A. Pope, R. Scranton, U. Seljak, R. K. Sheth, A. Stebbins, A. S. Szalay, I. Szapudi, L. Verde, Y. Xu, J. Annis, N. A. Bahcall, J. Brinkmann, S. Burles, F. J. Castander, I. Csabai, J. Loveday, M. Doi, M. Fukugita, J. R. Gott III, G. Hennessy, D. W. Hogg, Ž. Ivezić, G. R. Knapp, D. Q. Lamb, and D. G. York, "The Three‐Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey," Astrophys. J. 606(2), 702–740 (2004). https://doi.org/10.1086/382125

A. Pradhan and H. Amirhashchi, "Dark energy model in anisotropic Bianchi type-III space-time with variable EoS parameter," Astrophys. Space Sci. 332(2), 441–448 (2010). https://doi.org/10.1007/s10509-010-0539-z

R. Chaubey and A. K. Shukla, "The anisotropic cosmological models in f(R, T) gravity with Λ(T)," Pramana 88(4) (2017). https://doi.org/10.1007/s12043-017-1371-6

D. M. Gusu and M. V. Santhi, "Analysis of Bianchi Type V Holographic Dark Energy Models in General Relativity and Lyra’s Geometry," Adv. High Energy Phys. 2021, 1–11 (2021). https://doi.org/10.1155/2021/8818590

S. Arora and P. K. Sahoo, "Energy conditions in f(Q, T) gravity," Phys. Scr. 95(9), 095003 (2020). https://doi.org/10.1088/1402-4896/abaddc

Singh JK, Pradhan A, Beesham A. Power law cosmology in modified theory with higher order curvature term. arXiv preprint arXiv:2304.09917. 2023 Apr 19. Available from: https://doi.org/10.48550/arXiv.2304.09917

J. K. Singh and R. Nagpal, "FLRW cosmology with EDSFD parametrization," Eur. Phys. J. C 80(4) (2020). https://doi.org/10.1140/epjc/s10052-020-7827-8

J. K. Singh, A. Singh, G. K. Goswami, and J. Jena, "Dynamics of a parametrized dark energy model in f(R,T) gravity," Ann. Phys. 2022, 168958. https://doi.org/10.1016/j.aop.2022.168958

How to Cite
Roy, S., Kayal, R., Ali, S., Bandyopadhyay, S., & Bhattacharya, D. (2023). A Study of Evolution of Cosmological Parameters Based on a Dark Energy Model in the Framework of Brans-Dicke Gravity. East European Journal of Physics, (3), 96-107. https://doi.org/10.26565/2312-4334-2023-3-07