Right after its birth, the Universe ballooned faster than light could cross it. This burst stretched tiny quantum jitters to the size of galaxies. It is usually assumed that after such stretching the jitters lose their quantum character and become ordinary, like ripples on water. But perhaps a quantum connection survived in them, and that connection is called entanglement. Entanglement is like a pair of coins that always land on opposite sides, even if you toss them in different cities.
In the early Universe, such pairs could be born from gravitational waves, or more precisely, from their smallest portions, gravitons. A graviton is like a photon, but it carries not light but the force of gravity. Every graviton has a polarization, that is, a direction of vibration, like a stretched string. If two gravitons are entangled, then the direction of vibration of one immediately determines the direction of vibration of the other, even if they have flown far apart.
The horizon of the Universe during inflation played the role of a measuring device. It gathered information about the path each fluctuation took, and thereby destroyed the quantum connection. This is similar to how observing a particle in an interferometer fixes its trajectory and destroys the interference. But even after such destruction, the correlation between polarizations persists, and it can be calculated from the statistics of the positions of four galaxies. Today this trace can be sought in data from sky surveys such as Euclid or DESI. If the signal is found, it will be the first direct proof that quantum mechanics operated on the scales of the entire Universe at the moment of its birth.
The cosmological horizon during inflation acts as a measuring device: it gathers information about which path a fluctuation took, and in doing so destroys quantum coherence. It is similar to how observing a particle in an interferometer pins down its trajectory.
The idea that the large-scale structure of the Universe stores quantum correlations echoes a motif from Greg Egan's novel Schild's Ladder, where the fundamental laws of physics turn out to be encoded in the geometry of spacetime.