We explore a nonstandard model for the Universe in which we take a vacuum solution of Einstein’s equation as background and introduce visible matter and radiation as perturbations. The perturbation theory is greatly simplified by using the mapping on the inner Schwarzschild solution. The resulting linear perturbation equations can be solved by power series. The solution leads to a finite energy density, but the pressure must be zero. A nonzero pressure comes in the exceptional case of spherical perturbation which gives the isotropic CMB perturbation. The model needs further exploration, in particular a quantitative treatment of CMB, to determine if it is fully consistent with our Universe.