The basic purpose of this communication, is to investigate the dynamical nature of Bianchi type-I universe with perfect fluid content in Sáez-Ballester (SB) theory (Phys. Lett. A 113:467–470, 1986 ). We got the solution of modified Einstein’s field equations (EFEs) by considering the bilinearly varying deceleration parameter (BVDP) and the gravitational constant ( G ) $(G)$ as a power function of average scale factor a ( t ) $a(t)$ . We assumed that BVDP is function of cosmic time with q ( t ) = α ( 1 − t ) 1 + t $q(t)=\frac{\alpha (1-t)}{1+t}$ , α ≥ 0 $\alpha \geq 0$ . Our finding suggests that present universe has had transitional phase of expansion which was decelerating in the past and is accelerating phase at present time. We also observed that the DE parameter ( Λ ) $(\Lambda )$ and energy density parameter ( ρ ) $(\rho )$ are decreasing with respect to cosmic time and converge to a very small value at the late time. This result is in strong agreement with recent observations. Physical and geometric properties of the cosmological parameters are also presented in the communication.

中文翻译：

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Sáez-Ballester 理论中具有双线性变减速参数的宇宙学模型

本次交流的基本目的是在 Sáez-Ballester (SB) 理论 (Phys. Lett. A 113:467–470, 1986) 中研究具有完美流体含量的 Bianchi I 型宇宙的动力学性质。我们通过考虑双线性变化的减速参数 (BVDP) 和引力常数 ( G ) $(G)$ 作为平均比例因子 a ( t ) $a(t) 的幂函数，得到了修正爱因斯坦场方程 (EFE) 的解)$ 。我们假设 BVDP 是宇宙时间的函数，其中 q ( t ) = α ( 1 − t ) 1 + t $q(t)=\frac{\alpha (1-t)}{1+t}$ , α ≥ 0 $\alpha \geq 0$ 。我们的发现表明，现在的宇宙有膨胀的过渡阶段，过去是减速的，现在是加速的阶段。我们还观察到 DE 参数 (Λ)$(\Lambda)$ 和能量密度参数 (ρ)$(\rho)$ 相对于宇宙时间正在减少，并在后期收敛到一个非常小的值。这一结果与最近的观察结果非常一致。宇宙学参数的物理和几何特性也在通信中呈现。