  We investigate a quasi-local energy naturally introduced by Kodama's
prescription for a spherically symmetric space-time with a positive
cosmological constant $\Lambda$. We find that this quasi-local energy is well
behaved inside a cosmological horizon. However, when there is a scalar field
with a long enough Compton wavelength, the quasi-local energy diverges in the
course of its time evolution outside the cosmological horizon. This means that
the quasi-local energy has a meaning only inside the cosmological horizon.
