A conserved variable in the perturbed hydrodynamic world model

We introduce a scalar-type perturbation variable $\mathrm{\Phi }$ which is conserved in the large-scale limit considering general sign of three-space curvature ($K$), the cosmological constant ($\mathrm{\Lambda }$), and time varying equation of state. In a pressureless medium $\mathrm{\Phi }$ is {\it exactly conserved} in all scales.