Abstract
The present study is outcome of investigation of Bianchi type-I cosmological model in Sáez-Ballester theory of gravity with variable deceleration parameter. Here, we have also considered variable cosmological constant \(\Lambda\) which may be a probable candidate to discuss dark energy. The solution of the field equations has been found using variable deceleration parameter i.e. \(q=-1+\beta H\) (with \(\beta\) as a positive constant and \(H\) as Hubble parameter) (Tiwari et al. in Eur. Phys. J. Plus 132:1–9, 2017) and suitable assumption of variable form of cosmological constant. We have expressed cosmological parameters such as Hubble parameter, deceleration parameter, energy density, pressure, cosmological constant and equation of state (EoS) in terms of redshift parameter and presented their dynamical behaviour graphically. In addition to Hubble parameter and deceleration parameter, the redshift variation of other higher order cosmographic parameters such as jerk, snap and lerk parameters has also been observed. The evolution of \((s,r)\) and \((q,r)\) trajectories has been examined to study different phases of the universe. Inspired by the study carried by Magana et al. (Mon. Not. R. Astron. Soc. 476(1), 1036, 2018), which consists of updated compilation of 51 points of homogenized and model-independent observational Hubble data, we have decided to use the same data for proposed study related with the expansion of the universe. Using these 51 values of observed Hubble measurements and performing \(\chi^{2}\) test, we have found the best suitable value of model parameter \(\beta\) and \(H_{0}\) (present value of Hubble parameter). The authors have noted that the obtained outcomes coincide with the modern cosmological observational data.
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References
Abers, E., Lee, B.: Guage theories. Phys. Rep. 9, 1–141 (1973)
Aditya, Y., Reddy, D.R.K.: Anisotropic new holographic dark energy model in Sáez–Ballester theory of gravitation. Astrophys. Space Sci. 363(10), 1–11 (2018)
Akarsu, Ö., Dereli, T.: Cosmological models with linearly varying deceleration parameter. Int. J. Theor. Phys. 51(2), 612 (2012)
Akarsu, Ö., Kumar, S., Myrzakulov, R., Sami, M., Xu, L.: Cosmology with hybrid expansion law: scalar field reconstruction of cosmic history and observational constraints. J. Cosmol. Astropart 2014(01), 022 (2014)
Allen, S.W., et al.: Constraints on dark energy from Chandra observations of the largest relaxed galaxy clusters. Mon. Not. R. Astron. Soc. 353, 457–467 (2004)
Arbab, A.I.: FRW-type universe with vacuum energy density. Gravit. Cosmol. 8, 227 (2002)
Bennet, C.L., et al.: First year Wilkinson microwave anisotropy probe (WMAP) observations: preliminary maps and basic results. Astrophys. J. Suppl. 148, 1 (2003)
Brans, C., Dicke, R.H.: Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124(3), 925 (1961)
Capozziello, S., Carloni, S., Troisi, A.: Quintessence without scalar fields. Recent Res. Dev. Astron. Astrophys. 1, 625 (2003). astro-ph/0303041
Chawla, C., Mishra, R.K., Pradhan, A.: String cosmological models from early deceleration to current acceleration phase with varying G and \(\Lambda\). Eur. Phys. J. Plus 127(11), 137 (2012)
Chen, C.M., Kao, W.F.: Stability analysis of anisotropic inflationary cosmology. Phys. Rev. D 64, 124019 (2001)
Harko, T., Lobo, F.S., Nojiri, S., Odintsov, S.D.: f (R, T) gravity. Phys. Rev. D 84(2), 024020 (2011)
Katore, S.D., Gore, S.V.: \(\Lambda\)CDM cosmological models with quintessence in \(f (R)\) theory of gravitation. J. Astrophys. Astron. 41, 1–15 (2020)
Langacker, P.: Grand unified theories and proton decay. Phys. Rep. 72, 185 (1981)
Magana, J., Amante, M.H., Garcia-Aspeitia, M.A., Motta, V.: The Cardassian expansion revisited: constraints from updated Hubble parameter measurements and type Ia supernova data. Mon. Not. R. Astron. Soc. 476(1), 1036 (2018)
Mishra, R., Chand, A.: Cosmological models in alternative theory of gravity with bilinear deceleration parameter. Astrophys. Space Sci. 361(8), 259 (2016)
Mishra, R.K., Dua, H., Chand, A.: Bianchi-III cosmological model with BVDP in modified theory. Astrophys. Space Sci. 363(6), 112 (2018)
Mishra, R.K., Dua, H.: Bulk viscous string cosmological models in Sáez-Ballester theory of gravity. Astrophys. Space Sci. 364(11), 195 (2019)
Mishra, R.K., Dua, H.: Phase transition of cosmological model with statistical techniques. Astrophys. Space Sci. 365(7), 1–13 (2020)
Mishra, R.K., Chand, A.: Cosmological models in Sáez-Ballester theory with bilinear varying deceleration parameter. Astrophys. Space Sci. 365, 1–9 (2020)
Mishra, R.K., Dua, H.: Evolution of FLRW universe in Brans-Dicke gravity theory. Astrophys. Space Sci. 366(1), 1–13 (2021)
Naidu, R.L., Aditya, Y., Raju, K.D., Vinutha, T., Reddy, D.R.K.: Kaluza-Klein FRW dark energy models in Sáez-Ballester theory of gravitation. New Astron. 85, 101564 (2021)
Nojiri, S., Odintsov, S.D.: Modified gravity with negative and positive powers of curvature: unification of inflation and cosmic acceleration. Phys. Rev. D 68(12), 123512 (2003)
Nojiri, S., Odintsov, S.D.: Introduction to modified gravity and gravitational alternative for dark energy. Int. J. Geom. Methods Mod. Phys. 4, 145 (2007)
Padmanabhan, T.: Cosmological constant - the weight of the vacuum. Phys. Rep. 380, 235–320 (2003)
Perlmutter, S., et al.: Measurements of the cosmological parameters \(\Omega\) and \(\Lambda\) from the first seven supernovae at \(z \geq 0.35\). Astrophys. J. 483, 565 (1997)
Perlmutter, S., et al.: Discovery of supernova explosion at the half the age of the universe. Nature 391, 51 (1998)
Rasouli, S.M.M., Pacheco, R., Sakellariadou, M., Moniz, P.V.: Late time cosmic acceleration in modified Sáez–Ballester theory. Phys. Dark Universe 27, 100446 (2020)
Riess, A., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)
Sáez, D., Ballester, V.J.: A simple coupling with cosmological implications. Phys. Lett. A 113(9), 467–470 (1986)
Sahni, V., Saini, T.D., Starobinsky, A.A., Alam, U.: Statefinder—a new geometrical diagnostic of dark energy. J. Exp. Theor. Phys. 77(5), 201 (2003)
Santhi, M.V., Sobhanbabu, Y.: Bianchi type-III Tsallis holographic dark energy model in Sáez-Ballester theory of gravitation. Eur. Phys. J. C 80(12), 1–15 (2020)
Singh, T., Agrawal, A.K.: Some Bianchi-type cosmological models in a new scalar-tensor theory. Astrophys. Space Sci. 182(2), 289–312 (1991)
Tegmark, M., et al.: Cosmological parameters from SDSS and WMAP. Phys. Rev. D 69, 103501 (2004)
Tiwari, R.K., Beesham, A., Shukla, B.K.: Cosmological models with viscous fluid and variable deceleration parameter. Eur. Phys. J. Plus 132(1), 1–9 (2017)
Tiwari, R.K., Sofuoglu, D.: Quadratically varying deceleration parameter in \(f(R,T)\) gravity. Int. J. Geom. Methods Mod. 17(10), 2030003-1315 (2020)
Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972)
Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989)
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The authors are highly thankful to the anonymous referee for his valuable comments/suggestions to improve this manuscript.
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Mishra, R.K., Dua, H. Bianchi type-I cosmological model in Sáez-Ballester theory with variable deceleration parameter. Astrophys Space Sci 366, 47 (2021). https://doi.org/10.1007/s10509-021-03952-4
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DOI: https://doi.org/10.1007/s10509-021-03952-4