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 Universes beginning, a sort of cosmic quantum hair.
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