  We examine various implications from a dynamical and chemical model of
globular clusters (GCs), which successfully reproduces the observed abundance
patterns and the multiple populations of stars in these systems assuming
chemical enrichment from fast rotating massive stars. Using the model of
Decressin et al. (2007) we determine the ratio between the observed,
present-day mass of globular clusters and their initial stellar mass as a
function of the stellar initial mass function (IMF). We also compute the mass
of low-mass stars ejected, and the amount of hydrogen ionising photons emitted
by the proto globular clusters. Typically, we find that the initial masses of
GCs must be ~8-10 times (or up to 25 times, if second generation stars also
escape from GCs) larger than the present-day stellar mass. The present-day
Galactic GC population must then have contributed to approximately 5-8%
(10-20%) of the low-mass stars in the Galactic halo. We also show that the
detection of second generation stars in the Galactic halo, recently announced
by different groups, provides a new constraint on the GC initial mass function
(GCIMF). These observations appear to rule out a power-law GCIMF, whereas they
are compatible with a log-normal one. Finally, the high initial masses also
imply that GCs must have emitted a large amount of ionising photons in the
early Universe. Our results reopen the question on the initial mass function of
GCs, and reinforce earlier conclusions that old GCs could have represented a
significant contribution to reionise the inter-galactic medium at high
redshift.
