We are working on applications of the Schwarzschild metric to the cosmos. Here we have calculated the curvature of space-time in an isotropic and homogeneous universe with a constant energy density, relating this universe to the Schwarzschild metric using the Birkhoff-Jebsen theorem. Already in this metric it is possible to calculate gaussian curvatures and thus we have found a solution to this problem. The result 0,1.10-52 m-2, is very close to zero and this agrees with the opinion of many scientists. To reach this result, we have found an equation that relates the Gaussian curvature of the space-time of the Schwarzschild model with several cosmic parameters and through it and the Birkhoff-Jebsen theorem we have established a relationship between the Schwarzschild metric and the universe of the standard cosmological model. This has allowed us to calculate the proportionality factor between curvature and mass density. With this, calculating the curvature of space-time is immediate.