Radial age gradients hold the cumulative record of the multitude of physical processes driving the build-up of stellar populations and the ensuing star formation (SF) quenching process in galaxy bulges, therefore potentially sensitive discriminators between competing theoretical concepts on bulge formation and evolution. Based on spectral modeling of integral field spectroscopy data from the CALIFA survey, we derive mass- and light-weighted stellar age gradients ($ abla$(t,B)L,M) within the photometrically determined bulge radius (RB) of a representative sample of local face-on late-type galaxies that span 2.6 dex in stellar mass. Our analysis documents a trend for decreasing $ abla$(t,B)L,M with increasing M,T, with high-mass bulges predominantly showing negative age gradients and vice versa. The inversion from positive to negative $ abla$(t,B)L,M occurs at logM,T ~ 10, which roughly coincides with the transition from lower-mass bulges whose gas excitation is powered by SF to bulges classified as Composite, LINER or Seyfert. We discuss two limiting cases for the origin of radial age gradients in massive LTG bulges. The first assumes that the stellar age in the bulge is initially spatially uniform, thus the observed age gradients arise from an inside-out SF quenching (ioSFQ) front that is radially expanding with a mean velocity vq. In this case, the age gradients translate into a slow ioSFQ that lasts until z~2, suggesting mild negative feedback by SF or an AGN. If negative age gradients in massive bulges are not due to ioSFQ but primarily due to their inside-out formation process, then the standard hypothesis of quasi-monolithic bulge formation has to be discarded in favor of a scenario that involves gradual buildup of stellar mass over 2-3 Gyr through, e.g., inside-out SF and inward migration of SF clumps from the disk. In this case, rapid AGN-driven ioSFQ cannot be ruled out.
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