LAUSR

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.