Quasi-local energy flux through cosmological dynamical horizons

Hoi-Lai Yu, Roh-Suan Tung, Chung-Hsien Chou

We apply and test the quasi-local energy flux expression for dynamically evolving spacetime obtained recently to FRW cosmology. It turns out the obtained energy flux flowing into the cosmological dynamical horizon is exactly the total energy changes during cosmological expansion given by the continuity and the Friedmann energy equation. This test not only confirm the validity of the energy flux expression but also help to clarify some misconceptions exits in the literature about the correct treatment of the boundary surface term when spacetime evolves dynamically, namely, the boundary term won't change the dynamics of the evolving universe at all by any mean. We have also observed an interesting duality between black-hole dynamical horizons and cosmological dynamical horizons.