  In this work we extend the work on the recently discovered role of Cosmic
Rays (CRs) in regulating the average CO/$\rm H_2$ abundance ratio in molecular
clouds (and thus their CO line visibility) in starburst galaxies, and find that
it can lead to a CO-poor/CI-rich $\rm H_2 $ gas phase even in environments with
Galactic or in only modestly enhanced CR backgrounds expected in ordinary
star-forming galaxies. Furthermore, the same CR-driven astro-chemistry raises
the possibility of a widespread phase transition of molecular gas towards a
CO-poor/CI-rich phase in: a) molecular gas outflows found in star-forming
galaxies, b) active galactic nuclei (AGNs), and c) near synchrotron-emitting
radio jets and the radio-loud cores of powerful radio galaxies. For main
sequence galaxies we find that CRs can render some of their molecular gas mass
CO-invisible, compounding the effects of low metallicities. Imaging the two
fine structure lines of atomic carbon with resolution high enough to search
beyond the CI/CO-bright line regions associated with central starbursts can
reveal such a CO-poor/CI-rich molecular gas phase, provided that relative
brightness sensitivity levels of $T_b$(CI $1-0$)/$T_b$(CO $J=1-0$)$\sim $0.15
are reached. The capability to search for such gas in the Galaxy is now at hand
with the new high-frequency survey telescope HEAT deployed in Antarctica and
future ones to be deployed in Dome A. ALMA can search for such gas in
star-forming spiral disks, galactic molecular gas outflows and the CR-intense
galactic and circumgalactic gas-rich environments of radio-loud objects.
