2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34028Presented cosmological model is 3D brane world sheet moved in extra dimension with variable scale factor. Analysis of the geodesic motion of the test particle gives settle explanation of the Pioneer effect. It is found that for considered metric the solution of the semi-classical Einstein equations with various parameters conforms to isotropic expanded and anisotropic stationary universe.General Relativity and Quantum Cosmologytext