Dark matter scenarios with multiple spin-2 fields
  We study ghost-free multimetric theories for $(N+1)$ tensor fields with a
coupling to matter and maximal global symmetry group $S_N\times(Z_2)^N$. Their
mass spectra contain a massless mode, the graviton, and $N$ massive spin-2
modes. One of the massive modes is distinct by being the heaviest, the
remaining $(N-1)$ massive modes are simply identical copies of each other. All
relevant physics can therefore be understood from the case $N=2$. Focussing on
this case, we compute the full perturbative action up to cubic order and derive
several features that hold to all orders in perturbation theory. The lighter
massive mode does not couple to matter and neither of the massive modes decay
into massless gravitons. We propose the lighter massive particle as a candidate
for dark matter and investigate its phenomenology in the parameter region where
the matter coupling is dominated by the massless graviton. The relic density of
massive spin-2 can originate from a freeze-in mechanism or from gravitational
particle production, giving rise to two different dark matter scenarios. The
allowed parameter regions are very different from those in scenarios with only
one massive spin-2 field and more accessible to experiments.
