Spatially flat matter-dominated universe filled with barotropic causal bulk viscous fluid: a symmetry-based approach

We have studied a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model with an additional assumption that the universe is filled with barotropic causal bulk viscous fluid. The bulk viscous coefficient of the fluid is related to the energy density $\left(\rho \right)$ and relaxation time $\left(\tau \right)$ by the relation $\zeta =c_b^2\tau \rho$. We have used a truncated version of the transport equation for the viscous pressure. The expansion rate of such a spatially flat FLRW universe is governed by the well-known modified Painlevé–Ince equation. We find that the Lie symmetry corresponding to scale invariance gives the power-law solution for this model equation from invariant curve condition. For the value of $c_b\sim 0.79$, our result satisfies the present experimental value $\sim -0.46$ of the deceleration parameter (q) for $N=\frac{1}{\tau H}=1$. The result obtained for the relaxation time $\left(\tau \right)$ which is of the order of the Hubble time supports the necessary condition for successful inflation. Our study not only shows the role of the bulk viscosity for the present accelerating expansion $(q<0)$ but also predicts an age of around $\sim 25Gyr$, which solves the age problem of the present universe. (paper)