  We consider the fluctuations in the number of particles in a box of size L^d
in Z^d, d>=1, in the (infinite volume) translation invariant stationary states
of the facilitated exclusion process, also called the conserved lattice gas
model. When started in a Bernoulli (product) measure at density rho, these
systems approach, as t goes to infinity, a "frozen" state for rho<=rho_c, with
rho_c=1/2 for d=1 and rho_c<1/2 for d>=2. At rho=rho_c the limiting state is
hyperuniform, that is, the variance of the number of particles in the box grows
slower than L^d. We give a general description of how the variances at
different scales of L behave as rho increases to rho_c. On the largest scale,
L>>L_2, the fluctuations are normal (in fact the same as in the original
product measure), while in a region L_1<<L<<L_2, with both L_1 and L_2 going to
infinity as rho increases to rho_c, the variance grows faster than normal. For
1<<L<<L_1 the variance is the same as in the hyperuniform system. (All results
discussed are rigorous for d=1 and based on simulations for d>=2.)
