"Big wigs" is a phrase that means people in positions of power or influence. There are several synonyms that can be used in place of "big wigs," including "movers and shakers," "heavyweights," "power brokers," "tycoons," "magnates," and "captains of industry." These words all indicate individuals who have significant sway in their respective fields. Other options include "influencers," "high-ups," "top shots," "big shots," and "big cheeses." Regardless of which term is used, it is clear that these individuals hold a great deal of power and influence within whatever sphere they operate in.