  de Sitter--G\"odel--de Sitter phase transition(dGd) is a possible geometrical
phase transition in the very early universe. It induces fluctuations with
possibly observable traces on matter and radiation fields. Here we present a
simulation based on dGd to investigate possible perturbations which could be
along with the standard inflationary fluctuations in the cosmic microwave
background (CMB) and distribution of the large-scale structure. The power
spectrum of perturbations is characterized by a parameter pair, labeled here as
($p_1, p_2$). With {\it Planck} observations we find
$p_1=0.008^{+0.003}_{-0.008}$ and $p_2= 0.002^{+0.001}_{-0.002}$ consistent
with pure inflationary power spectrum and no hint for the dGd transition. Also,
it is estimated future large-scale surveys such as Euclid and SKA can further
tighten the constraints up to an order of magnitude and probe the physics of
the early universe with much higher precision.
