The initial conditions of star formation: cosmic rays as the fundamental
  regulators
  Cosmic rays (CRs) control the thermal, ionization and chemical state of the
dense H_2 gas regions that otherwise remain shielded from far-UV and optical
stellar radiation propagating through the dusty ISM of galaxies. It is in such
CR-dominated regions (CRDRs) rather than Photon-dominated regions (PDRs) of H_2
clouds where the star formation initial conditions are set, making CRs the
ultimate star-formation feedback factor in galaxies, able to operate even in
their most deeply dust-enshrouded environments. CR-controlled star formation
initial conditions naturally set the stage for a near-invariant stellar Initial
Mass Function (IMF) in galaxies as long as their average CR energy density
U_{CR} permeating their molecular ISM remains within a factor of ~10 of its
Galactic value. Nevertheless, in the extreme environments of the compact
starbursts found in merging galaxies, where U_{CR}\sim(few)x10^{3}U_{CR,Gal},
CRs dramatically alter the initial conditions of star formation. In the
resulting extreme CRDRs H_2 cloud fragmentation will produce far fewer low mass
(<8 M_{sol}) stars, yielding a top-heavy stellar IMF. This will be a generic
feature of CR-controlled star-formation initial conditions, lending a physical
base for a bimodal IMF during galaxy formation, with a top-heavy one for
compact merger-induced starbursts, and an ordinary IMF preserved for star
formation in isolated gas-rich disks. In this scheme the integrated galactic
IMFs (IGIMF) are expected to be strong functions of the star formation history
of galaxies.
