  A classification of bosonic on- and off-shell modes on a cosmological quantum
space-time solution of the IIB matrix model is given, which leads to a
higher-spin gauge theory. In particular, the no-ghost-theorem is established.
The physical on-shell modes consist of 2 towers of higher-spin modes, which are
effectively massless but include would-be massive degrees of freedom. The
off-shell modes consist of 4 towers of higher-spin modes, one of which was
missing previously. The noncommutativity leads to a cutoff in spin, which
disappears in the semi-classical limit. An explicit basis allows to obtain the
full propagator, which is governed by a universal effective metric. The
physical metric fluctuations arise from would-be massive spin 2 modes, which
were previously shown to include the linearized Schwarzschild solution. Due to
the relation with ${\cal N}=4$ super-Yang-Mills, this is expected to define a
consistent quantum theory in 3+1 dimensions, which includes gravity.
