There are several synonyms for "approved by authority" that can be used interchangeably in various contexts. Some of these terms include authorized, sanctioned, endorsed, accredited, certified, ratified, and validated. All of these terms carry the same connotation of being approved or affirmed by an established authority. For instance, if a product is accredited, it means that it has been deemed to meet certain standards by the relevant authority. Similarly, if a document is validated, it means that it has been confirmed as authentic and verified by the relevant authority. In summary, all these synonyms can be used to describe something that has received official recognition or approval from an authoritative body.