  By adopting a $T$-matrix-based method within the $G_0G$ approximation for the
pair susceptibility, we study the effects of the pairing fluctuation on the
three-dimensional spin-orbit coupled Fermi gases at finite temperature. The
critical temperatures of the superfluid/normal phase transition are determined
for three different types of spin-orbit coupling (SOC): (1) the extreme oblate
(EO) or Rashba SOC, (2) the extreme prolate (EP) or equal Rashba-Dresselhaus
SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence
of the critical temperature signals a crossover from BCS to BEC state; at
strong SOC limit, the critical temperature recover those of ideal BEC of
rashbons. The pairing fluctuation induces a pseudogap in the fermionic
excitation spectrum in both superfluid and normal phases. We find that, for EO-
and S-type SOC, even at weak coupling, sufficiently strong SOC can induce
sizable pseudogap. Our research suggests that the spin-orbit coupled Fermi
gases may open new means to the study of the pseudogap formation in fermionic
systems.
