Hawking-like radiation as tunneling from the apparent horizon in a FRW Universe

TL;DR

This paper investigates Hawking-like radiation in an FRW universe using tunneling methods, revealing a novel relationship between tunneling probability and entropy change, with both spatial and temporal contributions to the tunneling amplitude.

Contribution

It introduces a canonical invariant tunneling amplitude for FRW spacetime, accounting for both spatial and temporal parts, and clarifies the entropy change sign difference in cosmological horizons.

Findings

Derived the correct Hawking-like temperature for FRW universe.

Found the tunneling amplitude includes both spatial and temporal contributions.

Established the relation mma  al S with a negative sign, differing from black hole results.

Abstract

We study Hawking-like radiation in a Friedmann-Robertson-Walker (FRW) universe using the quasi-classical WKB/tunneling method which pictures this process as a "tunneling" of particles from behind the apparent horizon. The correct temperature of the Hawking-like radiation from the FRW spacetime is obtained using a canonical invariant tunneling amplitude. In contrast to the usual quantum mechanical WKB/tunneling problem where the tunneling amplitude has only a spatial contribution, we find that the tunneling amplitude for FRW spacetime (i.e. the imaginary part of the action) has both spatial and temporal contributions. In addition we study back reaction and energy conservation of the radiated particles and find that the tunneling probability and change in entropy, ${\cal S}$ are related by the relationship: $\Gamma\propto\exp[-\Delta {\cal S}]$ which differs from the standard result $\Gamma\propto\exp[\Delta {\cal S}]$. By regarding the whole FRW universe as an isolated adiabatic system the change in the total entropy is zero. Then splitting the entropy between interior and exterior parts of the horizon ($\Delta {\cal S}_{total}=\Delta {\cal S}_{int} + \Delta {\cal S}_{ext}=0$), we can explain the origin of the minus sign difference with the usual result: our $\Delta {\cal S}$ is for the interior region while the standard result from black hole physics is for the exterior region.