  Future cosmological surveys will probe the expansion history of the universe
and constrain phenomenological models of dark energy. Such models do not
address the fine-tuning problem of the vacuum energy, i.e. the cosmological
constant problem (c.c.p.), but can make it spectacularly worse. We show that
this is the case for 'interacting dark energy' models in which the masses of
the dark matter states depend on the dark energy sector. If realised in nature,
these models have far-reaching implications for proposed solutions to the
c.c.p. that require the number of vacua to exceed the fine-tuning of the vacuum
energy density. We show that current estimates of the number of flux vacua in
string theory, $N_{\rm vac} \sim {\cal O}(10^{272,000})$, is far too small to
realise certain simple models of interacting dark energy \emph{and} solve the
cosmological constant problem anthropically. These models admit distinctive
observational signatures that can be targeted by future gamma-ray
observatories, hence making it possible to observationally rule out the
anthropic solution to the cosmological constant problem in theories with a
finite number of vacua.
