  The 3+1-dimensional Einstein-Hilbert action is obtained from the 1-loop
effective action on noncommutative branes in the IIB or IKKT matrix model. The
presence of compact fuzzy extra dimensions ${\cal K}$ as well as maximal
supersymmetry of the model is essential. The E-H action can be interpreted as
interaction of ${\cal K}$ with the space-time brane via IIB supergravity, and
the effective Newton constant is determined by the Kaluza-Klein scale of ${\cal
K}$. The bare matrix model defines a pre-gravity action with 2 derivatives less
than the induced E-H action, governing the cosmological regime. The
perturbative physics is confined to the space-time brane, which for covariant
quantum space-times includes all dof of gravity, as well as a tower of
higher-spin modes. The vacuum energy is given in terms of the symplectic volume
form, and hence does not act as cosmological constant.
