  We examine in detail the recent proposal that extreme
Cosmic-Ray-Dominated-Regions (CRDRs) characterize the ISM of galaxies during
events of high-density star formation, fundamentally altering its initial
conditions (Papadopoulos 2010). Solving the coupled chemical and thermal state
equations for dense UV-shielded gas reveals that the large cosmic ray energy
densities in such systems (U_{CR} (few)x(10^3-10^4) U_{CR,Gal}) will indeed
raise the minimum temperature of this phase (where the initial conditions of
star formation are set) from ~10K (as in the Milky Way) to (50-100)K. Moreover
in such extreme CRDRs the gas temperature remains fully decoupled from that of
the dust, with T_{kin} >> T_{dust}, even at high densities (n(H_2)~10^5--10^6
cm^{-3}), quite unlike CRDRs in the Milky Way where T_k T_{dust} when n(H_2) >=
10^5 cm^{-3}.
  These dramatically different star formation initial conditions will: a) boost
the Jeans mass of UV-shielded gas regions by factors of ~10--100 with respect
to those in quiescent or less extreme star forming systems, and b) "erase" the
so-called inflection point of the effective equation of state (EOS) of
molecular gas. Both these effects occur across the entire density range of
typical molecular clouds, and may represent {\it a new paradigm for all
high-density star formation in the Universe}, with cosmic rays as the key
driving mechanism, operating efficiently even in the high dust extinction
environments of extreme starbursts...
