Entropy Perturbations in N-flation
  In this paper we study the entropy perturbations in N-flation by using the
$\d\ma{N}$ formalism. We calculate the entropy corrections to the power
spectrum of the overall curvature perturbation $P_{\z}$. We obtain an analytic
form of the transfer coefficient $T^2_{\ma{R}\ma{S}}$, which describes the
correlation between the curvature and entropy perturbations, and investigate
its behavior numerically. It turns out that the entropy perturbations cannot be
neglected in N-flation, because the amplitude of entropy components is
approximately in the same order as the adiabatic one at the end of inflation
$T^2_{\ma{R}\ma{S}}\sim\ma{O}(1)$. The spectral index $n_S$ is calculated and
it becomes smaller after the entropy modes are taken into account, i.e., the
spectrum becomes redder, compared to the pure adiabatic case. Finally we study
the modified consistency relation of N-flation, and find that the
tensor-to-scalar ratio ($r\simeq0.006$) is greatly suppressed by the entropy
modes, compared to the pure adiabatic one ($r\simeq0.017$) at the end of
inflation.
