  We provide a very general argument showing that the Universe must have kept
its quantum memories from an epoch much earlier than $60$ e-foldings before the
end of inflation. The point is that a generic system of enhanced memory storage
capacity exhibits a phenomenon of memory burden. Due to its universal nature
this effect must be applicable to de Sitter since the latter has a maximal
memory storage capacity thanks to its Gibbons-Hawking entropy. The primordial
information pattern encoded in de Sitter memory initially costs very little
energy. However, because of Gibbons-Hawking evaporation, the memory burden of
the pattern grows in time and increasingly back reacts on the evaporation
process. After a finite time the memory burden becomes unbearable and de Sitter
quantum breaks. If inflation ended not long before its quantum break-time, the
imprints of the primordial memory pattern can be observable. This provides a
qualitatively new type of window in the Universe's beginning, a sort of cosmic
quantum hair.
