Date: 202202
Local time of day: 0001-0600
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Night
Aircraft: Regional Jet 900 (CRJ900)
Operator: Air Carrier
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Aircraft component: Pressurization Control System
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Troubleshooting; Situational Awareness
Second reporter function: First Officer
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft Other Automation; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Took Evasive Action; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Diverted; General Flight Cancelled / Delayed; General Maintenance Action
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: I was Pilot Flying on Aircraft X operating from ZZZ1 to ZZZ2. This was a reposition flight with just the required crew. During our climb out I selected speed mode and set Climb speed at 320 kts to prevent a high climb rate. While climbing through approximately F290 I noticed my relief differential press at 8.2 so I reduced thrust to reduce the differential pressure. The Cabin Altitude was approximately 3;700  ft. and climbing; climb rate was showing 3;500 FPM even thought I reduced thrust to get actual climb rate to below 1;500 FPM. While leveling off at FL340 we got the CABIN ALT caution message and it stayed illuminated even thought we were not climbing. We ran the QRH and but the CABIN ALT warning message came on followed by the PAX OXY caution. We advised ATC and descended to 8;000 ft. The message cleared at 8;000 ft. but due to the PAX OXY auto deploy we cancelled the [approach] and diverted to ZZZ after communicating with Dispatch and Maintenance.Due to excessive initial climb rate; airplane altitude increased above cabin Altitude limitation Make sure not to climb more than 1500 FPM especially at higher altitudes.


Second narrative: We were on a repo from ZZZ1-ZZZ2. Briefed not climbing too fast on ground and during the climb. We climbed at 320 kts and were in the process of leveling off keeping and eye on the cabin diff pressure which we hadn't been exceeding. Within 1;000 ft. of F320; cabin diff went yellow. We pulled QRH and followed procedure. Nothing stopped cabin pressure from climbing; so we both donned masks and started descending. Cabin pressure proceeded to climb to 12;000 ft.; even in our descent; and then went red. As we were descending; the passenger O2 masks dropped. We asked for immediate descent and continued down to 8;000 ft. as we were worried about potential structural issues we were unaware of. Cabin pressure finally stabilized. Ended emergency status and diverted to ZZZ.Assuming pressurization malfunction as we were monitoring during the climb.


Synopsis: CRJ900 flight crew reported a cabin altitude light during climb and elected to descend and divert to a precautionary landing.