Appears in collection : Symmetry in Geometry and Analysis

We establish the analog for real spherical varieties of the Scattering Theorem of Sakellaridis and Venkatesh for p-adic wavefront spherical varieties. This implies a Plancherel formula. We use properties of the Harish-Chandra homomorphism of Knop for invariant differential operators of the variety, special coverings of the variety and spectral projections. We have to make an analog of the Discrete Series Conjecture of Sakellaridis and Venkatesh.