  In this work we study the consequences of a longitudinal Bjorken expansion
and a Hubble-like temperature cooling scenario on a 1+1D non-linear model of
the diffusive dynamics of fluctuations in the net-baryon density. The
equilibrium behavior of the fluctuations is fully encoded in the temperature
dependence of the susceptibilities on the crossover side both in the vicinity
of the assumed location of the critical point and at vanishing baryo-chemical
potential in-line with lattice QCD calculations. We demonstrate the great
sensitivity of the fluctuation observables on the dynamics, in particular on
the diffusion length and the freeze-out conditions. While the critical signals
are visible and the critical region is broadened by the expansion, a too small
diffusion length can strongly reduce the amplitude of the signals. We propose
to search for significant anti-correlations of baryons at intermediate rapidity
experimentally and to map out the rapidity dependence of the fourth-order
cumulant, which in the presence of a critical point (and only in its presence)
has a pronounced minimum at intermediate rapidities.
