We report results from a large molecular line survey of Luminous Infrared Galaxies (L_{IR} >= 10^{11} L_sol) in the local Universe (z<=0.1), conducted during the last decade with the James Clerk Maxwell Telescope (JCMT) and the IRAM 30-m telescope. This work presents the CO and {13}CO line data for 36 galaxies, further augmented by multi-J total CO luminosities available for other IR-bright galaxies from the literature. This yields a sample of N=70 galaxies with the star-formation (SF) powered fraction of their IR luminosities spanning L_{IR} (10^{10}-2x10^{12}) L_sol and a wide range of morphologies. Simple comparisons of their available CO Spectral Line Energy Distributions (SLEDs) with local ones, as well as radiative transfer models discern a surprisingly wide range of average ISM conditions, with most of the surprises found in the high-excitation regime. These take the form of global CO SLEDs dominated by a very warm (T_{kin}>=100 K) and dense (n>=10^4 cm^{-3}) gas phase, involving galaxy-sized (~(few)x10^9 M_sol) gas mass reservoirs under conditions that would otherwise amount only ~1% of mass per typical SF molecular cloud in the Galaxy. Some of the highest excitation CO SLEDs are found in the so-called Ultra Luminous Infrared Galaxies and seem irreducible to ensembles of ordinary SF-powered regions. Highly supersonic turbulence and high cosmic ray (CR) energy densities rather than far-UV/optical photons or SNR-induced shocks from individual SF sites can globally warm the large amounts of dense gas found in these merger-driven starbursts and easily power their extraordinary CO line excitation.....
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