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We investigate the effects of topological order on the transitiontemperature, $T_c$, and response functions in fermionic superfluids with Rashbaspin-orbit coupling and a transverse Zeeman field in three dimensions. Ourcalculations, relevant to the ultracold atomic Fermi gases, includefluctuations beyond mean-field theory and are compatible with $f$-sum rules.Reminiscent of the $p_x + i p_y$ superfluid, the topological phase isstabilized when driven away from the Bose-Einstein condensation and towards theBCS limit. Accordingly, while experimentally accessible, $T_c$ is significantlysuppressed in a topological superfluid. Above $T_c$, the spin and densityresponse functions provide signatures of topological phases via therecombination or amplification of frequency dependent peaks.

Topological effects on transition temperatures and response functions in three-dimensional Fermi superfluids