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Phantom dark energy nature of bulk-viscosity universe in modified $f (Q)$ $f (Q)$ -gravity

Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura 281 406, India

Center for Theoretical Physics and Mathematics, IASE (Deemed to be University), Sardarshahar 331 403 (Churu), Rajasthan, India

E-mail Address: dcmaurya563@gmail.com

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Anirudh Pradhan

Centre for Cosmology, Astrophysics and Space Science, GLA University, Mathura 281 406, Uttar Pradesh, India

E-mail Address: pradhan.anirudh@gmail.com

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https://doi.org/10.1142/S0219887822501985Cited by:21 (Source: Crossref)

Abstract

This paper deals with an anisotropic cosmological model in the modified theory of $f (Q)$ $f (Q)$ -gravity filled with bulk-viscosity fluid. We investigated the modified $f (Q)$ $f (Q)$ -gravity with quadratic form $f (Q) = - α Q^{2}$ $f (Q) = - α Q^{2}$ , where $Q$ $Q$ is the non-metricity scalar and $α$ $α$ is a positive constant, in Locally-Rotationally Symmetric (LRS) Bianchi type- $I$ $I$ space time universe. We have solved the modified Einstein’s field equations with bulk-viscosity factor $ξ (t) = ξ_{0} H + ξ_{1} H^{2}$ $ξ (t) = ξ_{0} H + ξ_{1} H^{2}$ and obtained average scale factor $a (t) = k_{0} {[e_{1}^{k_{1} t} sech (k_{2} t)]}_{2}^{3}$ $a (t) = k_{0} {[e^{k_{1} t} sech (k_{2} t)]}^{3}$ where $k_{0}$ $k_{0}$ is a constant and $k_{1} = \frac{ξ_{1} {(m + 2)}^{2}}{108 α (2 m + 1)}$ $k_{1} = \frac{ξ_{1} {(m + 2)}^{2}}{108 α (2 m + 1)}$ , and $k_{2} = - \frac{(m + 2) \sqrt{ξ_{1} {(m + 2)}^{2} + 48 α ξ_{0} (2 m + 1)}}{108 α (2 m + 1)}$ $k_{2} = - \frac{(m + 2) \sqrt{ξ_{1} {(m + 2)}^{2} + 48 α ξ_{0} (2 m + 1)}}{108 α (2 m + 1)}$ . We have investigated the model in two cases $ξ_{0} = 0$ $ξ_{0} = 0$ and $ξ_{1} = 0$ $ξ_{1} = 0$ . We have found the best-fit values of model parameters with observational datasets like Union 2.1 compilation and Joint Light Curve Analysis (JLA) datasets by applying $R^{2}$ $R^{2}$ -test formula in curve-fitting. Using these best-fit values of model parameters, we have studied the cosmological parameter like Hubble parameter $H$ $H$ and deceleration parameter $q$ $q$ , equation of state (EoS) parameter, age of the present universe $t_{0}$ $t_{0}$ , etc. We have obtained a transit model (i.e. decelerating to accelerating in current) in the first case $ξ_{0} = 0$ $ξ_{0} = 0$ and a transit phase model from accelerating to decelerating in the second case $ξ_{1} = 0$ $ξ_{1} = 0$ . We have investigated the EoS parameter $ω_{v}$ $ω_{v}$ for bulk-viscosity and obtained the present values as $- 1.2 < ω_{v} < 2.5$ $- 1.2 < ω_{v} < 2.5$ , which is supported by the observational results. We have also analyzed energy conditions and statefinder parameters and found that our model approaches to LCDM model in the future.

Keywords:

AMSC: 83C15, 83F05, 83D05

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