  Anomaly-free perturbations of loop quantum cosmology with holonomy
corrections reveal an $\Omega$ -deformed spacetime structure,
$\Omega:=1-2\rho/\rho_c$, where $\Omega<0$ indicates a Euclidean-like space and
$\Omega>0$ indicates a Lorentz-like space. It would be reasonable to give the
initial value at the spacetime transition point, $\rho=\rho_c/2$, but we find
that it is impossible to define a Minkowski-like vacuum even for large $k$
modes at that time. However, if we loosen the condition and give the initial
value slightly after $\Omega=0$, e.g., $\Omega\simeq 0.2$, the vacuum state can
be well defined and, furthermore the slow roll approximation also works well in
that region. Both scalar and tensor spectra are considered in the framework of
loop quantum cosmology with holonomy corrections. We find that if the energy
density is not too small in relation to $\rho_c/2$ when the considered $k$ mode
crossing the horizon, effective theory can give a much smaller scalar power
spectrum than classical theory and the spectrum of tensor perturbations could
blueshift. But when compared to other observations, since the energy densities
when the modes crossed the horizon were significantly smaller than $\rho_c$,the
results we get agree with previous work in the literature and with the
classical inflation theory.
