Abstract
We consider radiation from cosmological apparent horizon in Friedmann–Lemaitre–Robertson–Walker (FLRW) model in a double-null coordinate setting. As the spacetime is dynamic, there is no timelike Killing vector, instead we have Kodama vector which acts as dynamical time. We construct the positive frequency modes of the Kodama vector across the horizon. The conditional probability that a signal reaches the central observer when it is crossing from the outside gives the temperature associated with the horizon.
Highlights
Horizon thermodynamics is an extensively studied subject which acts as a window between classical and quantum theories of gravity
The laws of black hole mechanics [1,2] first gave an indication that something other than classical general relativity is at work where a horizon exists
Hawking discovered [3] that a black hole horizon emits thermal radiation at a temperature κ, it’s surface gravity and what was thought as a mere coincidence was understood as the beginning of a new paradigm in physics
Summary
Horizon thermodynamics is an extensively studied subject which acts as a window between classical and quantum theories of gravity. For a more general Friedmann– Lemaitre–Robertson–Walker (FLRW) model, though the event horizon and particle horizon can be defined, there is no timelike Killing vector since the spacetime is dynamical. Double-null coordinates though familiar for a black hole, are not so frequently used in cosmology In these coordinates we have found the apparent horizon (trapping horizon) of FLRW spacetime using Hayward’s formalism. We find that the horizon temperature estimated by this method matches the result obtained by Faraoni [26] and Criscienzo et al [30] where the Hamilton– Jacobi tunneling method had been employed This method of calculating temperature associated with a trapping horizon was previously been introduced in [37,38] in the case of a black hole. Throughout the paper the speed of light c, reduced Planck constant hand Boltzmann constant kB are set equal to unity
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