The Safe at the Edge of the Universe ⚡ экспресс
The onset of information leakage from the de Sitter cosmological horizon via radiation from a single Hawking pair is studied. In a class of two-dimensional flowing geometries interpolating between AdS2 and dS2, probe states are constructed using local operators and modular conjugates. The operator algebra (centaur algebra) is extended to a type II∞ factor via the crossed product. This enables the computation of the entropy difference between the thermofield double (reference state) and the state with a pair. The resulting dependence describes a mini-Page curve with a minimum at τ≈β/8, interpreted as the time when quantum information begins to exit the horizon. In the microcanonical ensemble, the algebraic entropy coincides with the generalized entropy of the entanglement wedge cut tracking the emitted particle. The relative modular flow between states yields a Lyapunov exponent λ=2π/β, defining the scrambling time—the scale at which the pair's information becomes accessible to an observer in the static patch. The result quantitatively links information leakage to horizon dynamics and scrambling.
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.