Transit timing variations in the WASP-4 planetary system

Transits in the planetary system WASP-4 were recently found to occur 80s earlier than expected in observations from the TESS satellite. We present 22 new times of mid-transit that confirm the existence of transit timing variations, and are well fitted by a quadratic ephemeris with period decay (-1.95 +/- 0.23) x 10^{-10} d per orbital period. We rule out instrumental issues, stellar activity, the Applegate mechanism and tidal effects as possible causes. The light-time effect is also not favoured. Apsidal precession is plausible but unproven. WASP-4b is only the third transiting hot Jupiter known to show transit timing variations to high confidence.