The paper presents late time cosmology in f (Q, T) gravity where the dark energy is purely geometric in nature. We start by employing a well motivated f (Q, T) gravity model, f (Q, T) = mQ n + bT where m, n and b are model parameters. Additionally we also assume the universe to be dominated by pressure-less matter which yields a power law type scale factor of the form a(t) = c2(At + c1) 1 A , where A = 3(8π + b) n(16π + 3b) and c1 & c2 are just integration constants. To investigate the cosmological viability of the model, constraints on the model parameters were imposed from the updated 57 points of Hubble data sets and 580 points of union 2.1 compilation supernovae data sets. We have thoroughly investigated the nature of geometrical dark energy mimicked by the parametrization of f (Q, T) = mQ n + bT with the assistance of statefinder diagnostic in {s, r} and {q, r} planes and also performed the Om-diagnostic analysis. The present analysis makes it clear-cut that f (Q, T) gravity can be promising in addressing the current cosmic acceleration and therefore a suitable alternative to the dark energy problem. Further studies in other cosmological areas are therefore encouraging to further investigate the viability of f (Q, T) gravity.

New high-precision observations are now possible to constrain different gravity theories. To examine the accelerated expansion of the Universe, we used the newly proposed f(Q, T) gravity, where Q is the non-metricity, and T is the trace of the energy–momentum tensor. The investigation is carried out using a parameterized effective equation of state with two parameters, m and n. We have also considered the linear form of $$f(Q,T)= Q+bT$$ f ( Q , T ) = Q + b T , where b is constant. By constraining the model with the recently published 1048 Pantheon sample, we were able to find the best fitting values for the parameters b, m, and n. The model appears to be in good agreement with the observations. Finally, we analyzed the behavior of the deceleration parameter and equation of state parameter. The results support the feasibility of f(Q, T) as a promising theory of gravity, illuminating a new direction towards explaining the Universe dark sector.

Bulk viscosity is the only viscous influence that can change the background dynamics in a homogeneous and isotropic universe. In the present work, we analyze the bulk viscous cosmological model with the bulk viscosity coefficient of the form $$\zeta =\zeta _0+\zeta _1H+\zeta _2\left( \frac{\dot{H}}{H}+H\right) $$ ζ = ζ 0 + ζ 1 H + ζ 2 H ˙ H + H where, $$\zeta _0$$ ζ 0 , $$\zeta _1$$ ζ 1 and $$\zeta _2$$ ζ 2 are bulk viscous parameters, and H is the Hubble parameter. We investigate the impact of the bulk viscous parameter on dynamics of the universe in the recently proposed Weyl-type f(Q, T) gravity, where Q is the non-metricity, and T is the trace of the matter energy–momentum tensor. The exact solutions to the corresponding field equations are obtained with the viscous fluid and the linear model of the form $$f(Q, T)=\alpha Q+\frac{\beta }{6\kappa ^2}T$$ f ( Q , T ) = α Q + β 6 κ 2 T , where $$\alpha $$ α and $$\beta $$ β are model parameters. Further, we constrain the model parameters using the 57 points Hubble dataset the recently released 1048 points Pantheon sample and the combination Hz + BAO + Pantheon, which shows our model is good congeniality with observations. We study the possible scenarios and the evolution of the universe through the deceleration parameter, the equation of state (EoS) parameter, the statefinder diagnostics, and the Om diagnostics. It is observed that the universe exhibits a transition from a decelerated to an accelerated phase of the universe under certain constraints of model parameters.