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.?
Be careful about your definition of the cosmological horizon. This term is normally used to mean the particle horizon and this is not an event horizon and does not radiate. A cosmological event horizon exists only in an accelerating universe. Since dark energy is accelerating the expansion of the universe we do have an event horizon, but it is currently farther away than the particle horizon and consequently is currently causally disconnected from us.
Strictly speaking the event horizon takes an infinite time to form, as measured by our clocks, though in practice the apparent horizon will be indistinguishable from a true horizon as soon as it moves inside the particle horizon, and we'll be able to see the Hawking radiation from it (in principle, though probably not in practice). The mechanism of Hawking radiation from the cosmological event horizon is exactly the same as the mechanism for the radiation from a black hole event horizon.