C525 Captain reported receiving an Aft Cabin Smoke Caution warning and chime during climb. Captain returned to the departure airport and a maintenance inspection found the smoke detector was faulty.

Narrative

After departing from ZZZ en-route to the ZZZ1 while climbing through about 30;000 feet; the Aft Cabin Smoke Caution illuminated and the 'AFT Cabin Smoke' verbal alert chimed. The Emergency Checklist Action was to land as soon as possible. The best landing field was ZZZ2 as it had plenty of runway length; good weather; and was about 20 miles away. I notified Air Traffic Control of my need to return as well as my requested airport of ZZZ2. ATC provided vectors to ZZZZZ and the ZZZZZ2 arrival followed by vectors to a visual approach for Runway XXL. A visual landing was made safely and the aircraft taxied to parking. After completing all checklist items; parking; and shutting down the engines; I inspected the aft baggage area and found no signs of any smoke either visually or by smell. The aircraft was then secured for the evening and maintenance was notified.A maintenance inspection of the aircraft was completed a few days later and found that the Aft Baggage Smoke detector was faulty. The part was replaced and system tested in accordance with the maintenance manual and procedures for the aircraft and the aircraft was returned to service.