  We study (p)reheating in alpha-attractor T-models of inflation, taking into
account both scalar fields present in these models: the inflaton and the
spectator. The two-field model has a negative field-space curvature which, at
the end of inflation, may lead to geometrical destabilization of the spectator
for small values of alpha<~10^(-3). We perform the instability (Floquet)
analysis of the linear dynamics and a fully non-linear lattice computations
with our numerical code, which we specifically designed for a class of
two-field models with non-canonical kinetic terms. We find that the
perturbations of the spectator field are much more unstable than the
perturbations of the inflaton field, so the dynamics of the early stages of
preheating is dominated by the evolution of the spectator perturbations. As a
result, the transition from the inflationary era to radiation domination era is
practically instantaneous and much faster than previously found in an effective
theory including only the inflaton field.
