On the Scarcity of Dense Cores ($n>10^{5}$ cm$^{-3}$) in High Latitude Planck Galactic Cold Clumps

High-latitude ($|b|>30^{\circ}$) molecular clouds have virial parameters that exceed 1, but whether these clouds can form stars has not been studied systematically. Using JCMT SCUBA-2 archival data, we surveyed 70 fields that target high-latitude Planck galactic cold clumps (HLPCs) to find dense cores with density of $10^{5}$-$10^{6}$ cm$^{-3}$ and size of $<0.1$ pc. The sample benefits from both the representativeness of the parent sample and covering densest clumps at the high column density end ($>1\times10^{21}$ cm$^{-2}$). At an average noise rms of 15 mJy/beam, we detected Galactic dense cores in only one field, G6.04+36.77 (L183), while also identifying 12 extragalactic objects and two young stellar objects. Compared to the low-latitude clumps, dense cores are scarce in HLPCs. With synthetic observations, the densities of cores are constrained to be $n_c\lesssim10^5$ cm$^{-3}$, should they exist in HLPCs. Low-latitude clumps, Taurus clumps, and HLPCs form a sequence where a higher virial parameter corresponds to a lower dense core detection rate. If HLPCs were affected by the Local Bubble, the scarcity should favor turbulence-inhibited rather than supernova-driven star formation. Studies of the formation mechanism of the L183 molecular cloud are warranted.