  In the early universe it is important to take into account quantum effect of
the gravity to explain the feature of the inflation. In this paper, we consider
the M-theory effective action which consists of 11 dimensional supergravity and
(Weyl)$^4$ terms. The equations of motion are solved perturbatively, and the
solution describes the inflation-like expansion in 4 dimensional spacetime.
Scalar and tensor perturbations around this background are evaluated
analytically and their behaviors are investigated numerically. If we assume
that these perturbations are constant at the beginning of the inflation,
spectral indices for scalar and tensor perturbations become almost scale
invariant.
