  The volume behind the black hole horizon was suggested as a holographic dual
for the quantum computational complexity of the boundary state in AdS/CFT. This
identification is strongly motivated by the switchback effect: a characteristic
delay of complexity growth in reaction to an inserted perturbation, modelled as
a shockwave in the bulk. Recent proposals of de Sitter (dS) holography suggest
that a dual theory could be living on a stretched horizon near the cosmological
horizon. We study how the spacetime volume behind the cosmological horizon in
Schwarzschild-dS space reacts to the insertion of shockwaves in an attempt to
characterize the properties of this dual theory. We demonstrate that a
switchback effect can be observed in dS space. That is, the growth of
complexity is delayed in reaction to a perturbation. This delay is longer for
earlier shocks and depends on a scrambling time which is logarithmic in the
strength of the shockwave and proportional to the inverse temperature of the
cosmological dS horizon. This behavior is very similar to what happens for AdS
black holes, albeit the geometric origin of the effect is different.
