  Apart from the assumption that the inflation started at an infinite time in
the past, the more realistic initial state of the quantum fluctuations is
described by a mixed quantum state imposed at a finite value of the initial
time. One of the most important non-trivial vacua is the $\alpha$-vacuum, which
is specified by a momentum cutoff $\Lambda$ \cite{Danielsson:2002kx}. As a
consequence, the initial condition is imposed at different initial times for
the different $k$-modes. This modifies the amplitude of the quantum
fluctuations, and thus the corresponding power spectra. In this paper, we
consider the imprint of the $\alpha$-vacuum state on the power spectrum of
scalar perturbations in a generic $f(R)$ gravity by assuming an ultraviolet
cutoff $\Lambda$. As a specific model, we consider the Starobinsky model and
find the trans-Planckian power spectrum. We find that the leading order
corrections to the scalar power spectra in $f(R)$ gravity have an oscillatory
behavior as in general relativity \cite{Lim}, and furthermore, the results are
in sufficient agreement with the $\Lambda$CDM model.
