  Analyzing the properties of dust and its evolution in the early phases of
star formation is crucial to put constraints on the collapse and accretion
processes as well as on the pristine properties of planet-forming seeds. We
analyze PdBI observations at 1.3 and 3.2 mm for 12 Class 0 protostars obtained
as part of the CALYPSO survey and derive dust emissivity index (beta) profiles
as a function of the envelope radius at 200-2000 au scales. Most of the
protostellar envelopes show low dust emissivity indices decreasing toward the
central regions. The decreasing trend remains after correction of the
(potentially optically-thick) central region emission, with surprisingly low
beta (lower than 1) values across most of the envelope radii of NGC1333-IRAS4A,
NGC1333-IRAS4B, SVS13B, and Serpens-SMM4. We discuss the various processes that
could explain such low and varying dust emissivity indices at envelope radii
200-2000 au. Our observations of extremely low dust emissivity indices could
trace the presence of large (mm-size) grains in Class 0 envelopes and a radial
increase of the dust grain size toward the inner envelope regions. While it is
expected that large grains in young protostellar envelopes could be built via
grain growth and coagulation, we stress that the typical timescales required to
build mm grains in current coagulation models are at odds with the youth of our
Class 0 protostars. Additional variations in the dust composition could also
partly contribute to the low beta we observe. The steepness of the beta radial
gradient depends strongly on the envelope mass, which might favor a scenario
where large grains are built in high density protostellar disks and transported
to the intermediate envelope radii, for example with the help of outflows and
winds.
