  Recently, a Hamilton-Jacobi method beyond semiclassical approximation in
black hole physics was developed by \emph{Banerjee} and
\emph{Majhi}\cite{beyond0}. In this paper, we generalize their analysis of
black holes to the case of Friedmann-Robertson-Walker (FRW) universe. It is
shown that all the higher order quantum corrections in the single particle
action are proportional to the usual semiclassical contribution. The
corrections to the Hawking-like temperature and entropy of apparent horizon for
FRW universe are also obtained. In the corrected entropy, the area law involves
logarithmic area correction together with the standard inverse power of area
term.
