Fluid-flow description of density irregularities in the Universe

A new derivation is given of two differential equations for the energy-density irregularities in the Universe, defined on a comoving hypersurface. One of them, a second-order equation, is valid generally and the other, a first-order equation, is valid when ${\nabla }^2$P is negligible where P is the pressure. The new derivation of these important equations uses the fluid-flow equations as advocated by Hawking in 1966, and is much simpler than the usual one involving metric perturbations. The regime of validity of the first-order equation is discussed in some detail.