Non-Linear f(Q,T) Gravity and the Late-Time Acceleration of the Universe

This study examines cosmic acceleration in the framework of f(Q,T) gravity and compares it to the standard ΛCDM model. It considers a generalized nonlinear form of the nonmetricity, expressed as f(Q,T)=−Q+α0Q2/H02+β0T+η0, where α0,β0, and η0 are constants, and H0 is the current value of the Hubble constant. In the solution process, we did not rely on any additional conditions to solve the field equations; instead, the field equations were reduced to a time-dependent closed system of nonlinear first-order coupled differential equations for H and ρ. Subsequently, these differential equations were converted to the redshift space for numerical integration alongside the Runge–Kutta method. Furthermore, the study demonstrates that the deceleration parameter q changes sign from being positive in an early period of time at high redshift values to a negative value, passing through a transitional redshift zt≈[0.766,0.769,0.771] and zt≈[0.521,0.770,1.010], reaching their current values at q0=[−0.61,−0.60,−0.59] and [−0.455,−0.595,−0.694] for different values of β0 and α0, respectively. Similarly, the effective equation of state weff shifted from the matter-dominated phase weff=0 at high redshift to a quintessence-like behavior at low redshift. Moreover, a super-accelerated or phantom-like regime with q0≃−1.59 and weff,0≃−1.40 was obtained when α0=0.55 and β0=0.60 were employed. The model analysis reveals that the universe is presently experiencing an accelerating expansion phase, propelled by a quintessence-type and phantom-like dark energy component, as corroborated by the Om(z) diagnostic test. The results obtained were strongly consistent with the concordance ΛCDM model.