The question of when information leaves the cosmological horizon is akin to the black hole information paradox. In a new study, a Hawking pair of quanta was modeled in a two-dimensional spacetime smoothly connecting AdS2 and dS2. Using the algebraic crossed product formalism, the entropy difference was computed, yielding a mini-Page curve: its minimum occurs at a time of about τ≈β/8, indicating the start of information leakage. The relative modular flow gives a Lyapunov exponent λ=2π/β — the scrambling time after which an observer in the static patch can read out the data. The discovery resembles a 'boiling' effect: at first the process is imperceptible, then a key moment arrives.
The cosmological horizon — the edge of the observable Universe, which is expanding at an accelerating rate — is like a safe with a timer. Information about what crosses this boundary doesn’t vanish but returns, albeit with a delay. Physicists have figured out how long this pause lasts.
Scientists constructed a model of curved spacetime and traced the birth of a pair of quantum particles: one flies away, the other falls inward. By tracking entropy (a measure of disorder), they found that its minimum occurs after 1/8 of the horizon’s traversal time — that’s when hidden information begins to leak out, as if the safe’s door cracks open.
This process echoes the black hole paradox, first described by Stephen Hawking: it is believed that black holes also release information as they evaporate. The safe-like horizon isn’t silent: it has a temperature of about 10⁻³⁰ K, many orders of magnitude colder than any known object. Detecting this thermal “breath” is still impossible, but the calculation gives an exact time when the horizon reveals its secrets.
🎯 Our cosmological horizon is a sphere with a radius of about 46 billion light-years. Inside it lies all the matter we will ever be able to observe. Its thermal radiation is so weak that its temperature (around 10⁻³⁰ K) is trillions of times lower than that of the coldest corners of space.