Are there studies on the effect of reduced CO2 levels on human cognition?

I see studies that indicate elevated CO2 levels (>>400ppm) can cause cognitive impairment.

Are there also studies that investigate the effects of cognition under low CO2 levels (<<400ppm)?

Answer

I can't think of any biological basis for such a study.

CO₂ is produced as a waste product of metabolism and exists in the blood and lungs at levels far higher than atmospheric levels (~100X). Relative to the air in the lungs, the atmospheric concentration of CO₂ might as well be zero.

Very high atmospheric CO₂ (relative to normal atmospheric levels) can have cognitive effects (among others) because it prevents CO₂ clearance from the lungs and therefore increases blood CO₂ (hypercapnia) and can cause respiratory acidosis.