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A classification of bosonic on- and off-shell modes on a cosmological quantumspace-time solution of the IIB matrix model is given, which leads to ahigher-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 areeffectively massless but include would-be massive degrees of freedom. Theoff-shell modes consist of 4 towers of higher-spin modes, one of which wasmissing previously. The noncommutativity leads to a cutoff in spin, whichdisappears in the semi-classical limit. An explicit basis allows to obtain thefull propagator, which is governed by a universal effective metric. Thephysical metric fluctuations arise from would-be massive spin 2 modes, whichwere previously shown to include the linearized Schwarzschild solution. Due tothe relation with ${\cal N}=4$ super-Yang-Mills, this is expected to define aconsistent quantum theory in 3+1 dimensions, which includes gravity.

Higher-spin kinematics & no ghosts on quantum space-time in Yang-Mills matrix models