In this article, we attempt to describe the cosmic late-time acceleration of the universe in the framework of $f(R,L_m)$ gravity, by using an effective equation of state, when bulk viscosity is taken into account. We presume a non-linear $f(R,L_m)$ functional form, specifically, $f(R,L_m)=\frac{R}{2}+L_m^{\alpha }$, where $\alpha$ is a free model parameter. We obtain the exact solution of our bulk viscous matter dominated $f(R,L_m)$ model, and then we utilize the combined $H\left(z\right)$ + Pantheon + Analysis datasets to estimate the best fit values of the free parameters of our model. Then, we characterize the behavior of the matter–energy density, effective pressure, and the equation of state (EoS) parameter, incorporating the viscous type fluid. The evolution profile of the effective EoS parameter depicts an acceleration phase of the cosmic expansion, whereas the pressure, with the effect of viscosity, exhibits negative behavior, that can lead to the accelerating expansion of the universe. Moreover, the cosmic matter–energy density shows the expected positive behavior. Further, we investigate the behavior of the statefinder parameters for the assumed $f(R,L_m)$ model. We find that the evolutionary trajectory of the given model lies in the quintessence region. In addition, we employ the Om diagnostic test, that indicates that our model exhibits quintessence behavior. Lastly, we check the energy condition criteria and find that the violation of SEC occurs in the past, whereas NEC and DEC satisfy the positivity criteria. We find that our $f(R,L_m)$ cosmological model, with the effect of bulk viscosity, provides a good fit of the recent observational data and can efficiently describe the cosmic expansion scenario.

This article explores matter bounce non-singular cosmology in f(R, L _m ) gravity. We consider two non-linear f(R, L _m ) functional forms, specifically, f ( R , L m ) = R 2 + λ R 2 + α L m and f ( R , L m ) = R 2 + L m β + γ representing a minimal coupling case. We derive the corresponding Friedmann-like equations for both the assumed models in the FLRW background, and then we present the impact of the model parameters along with the parameter of bouncing scale factor on the equation of state parameter, pressure, and the energy density. In addition, we examine the dynamical behavior of cosmographic parameters such as jerk, lerk, and snap parameters. Further, we find that the violation of the null energy condition along with the strong energy condition depicts the non-singular accelerating behavior, corresponding to both assumed non-linear f(R, L _m ) functions. Lastly, we present the behavior of the adiabatic speed of sound to examine the viability of the considered cosmological bouncing scenario.

In this article, we investigate scalar field cosmology in the coincident f(Q) gravity formalism. We calculate the motion equations of f(Q) gravity under the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a scalar field. We consider a non-linear f(Q) model, particularly f(Q) = − Q + α Q ⁿ , which is nothing but a polynomial correction to the Symmetric Teleparallel Equivalent to General Relativity (STEGR) case. Further, we assumed two well-known specific forms of the potential function, specifically the exponential from V(ϕ) = V ₀ e ^{−β ϕ} and the power-law form V(ϕ) = V ₀ ϕ ^−k . We employ some phase-space variables and transform the cosmological field equations into an autonomous system. We calculate the critical points of the corresponding autonomous systems and examine their stability behaviors. We discuss the physical significance corresponding to the exponential case for parameter values n = 2 and n = − 1 with β = 1, and n = − 1 with β = 3 . Moreover, we discuss the same corresponding to the power-law case for the parameter value n = − 2 and k = 0.16. We also analyze the behavior of corresponding cosmological parameters such as scalar field and dark energy density, deceleration, and the effective equation of state parameter. Corresponding to the exponential case, we find that the results obtained for the parameter constraints in Case III is better among all three cases, and that represents the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era via matter-dominated epoch. Further, in the power-law case, we find that all trajectories exhibit identical behavior, representing the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era. Lastly, we conclude that the exponential case shows better evolution as compared to the power-law case.