Constraining the Viscous Dark Energy Equation of State in <i>f</i> (<i>R</i>, <i>L</i>_<i>m</i>) Gravity

Abstract

In this article, we attempt to describe the cosmic late-time acceleration of the universe in the framework of f(R,Lm) gravity, by using an effective equation of state, when bulk viscosity is taken into account. We presume a non-linear f(R,Lm) functional form, specifically, f(R,Lm)=R2+Lmα, where α is a free model parameter. We obtain the exact solution of our bulk viscous matter dominated f(R,Lm) model, and then we utilize the combined H(z) + 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,Lm) 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,Lm) 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.

Keywords

• <i>f</i>(<i>R</i>,<i>L_m</i>) gravity
• bulk viscosity
• equation of state parameter
• observational datasets
• statefinder parameter
• Om diagnostic