Hawking showed that likewise black hole event horizon, cosmological horizons also radiates as they are at temperature proportional to surface gravity. Semi classical explanation exist about the Hawking radiation from event horizon. What mechanism exit for radiation from cosmological horizon.?

• “Event horizon in an accelerating universe radiates hawking radiation.” $~$In the case of a black hole, the black hole loses its mass and radiate Hawking radiation. But in the case of de Sitter horizon, where does the energy come from? – Forge Oct 20 '18 at 2:37
• OK, I understand that energy is not conserved because spacetime is not time-translation invariant.$~$ From what I understand, energy is not conserved only if pressure is not zero. – Forge Oct 21 '18 at 10:24