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The spherically symmetric solution for perfect fluid with homogeneous densityand inhomogeneous pressure has been considered. This solution is known asStephani solution. The matching of this solution and de Sitter solution hasbeen done on a hypersurface of constant time. The matching has been done forgeneral case and for particular cases (flat, closed, open universe). Anequality of the densities and a bound of the pressures have been shown on thematching hypersurface. Also, restrictions on some arbitrary functions have beenfound.

Matching of Stephani and de Sitter solutions on the hypersurface of constant time