# Tunneling of Massive/Massless Bosons From the Apparent Horizon of FRW Universe

## TL;DR

This paper studies Hawking radiation of vector bosons from the apparent horizon of an FRW universe using quantum tunneling, Proca equation, and Hamilton-Jacobi methods, confirming consistent Hawking temperature results.

## Contribution

It extends the tunneling method to vector particles in an FRW universe, including massive and massless bosons, using the Proca equation and Hamilton-Jacobi approach.

## Key findings

- Hawking temperature for vector particles matches scalar and Dirac cases.
- Proca equation solutions confirm tunneling probabilities.
- Results support universality of Hawking radiation across particle types.

## Abstract

In this article we investigate the Hawking radiation of vector particles from the apparent horizon of a Friedmann-Robertson-Walker (FRW) universe in the framework of quantum tunneling method. Furthermore we use Proca equation, a relativistic wave equation for a massive/massless spin-1 particle (massless $\gamma$ photons, weak massive $W^{\pm}$ and $Z^{0}$ bosons, strong massless gluons and $\rho$ and $\omega$ mesons) together with a Painlev\'{e} spacetime metric for the FRW universe. We solve the Proca equation via Hamilton-Jacobi (HJ) equation and the WKB approximation method. We recover the same result for the Hawking temperature associated with vector particles as in the case of scalar and Dirac particles tunnelled from outside to the inside of the apparent horizon in a FRW universe.