CO lines in high redshift galaxies: perspective for future mm instruments

Nearly 10 high redshift (z > 2) starburst galaxies have recently been detected in the CO lines, revealing the early presence in the universe of objects with large amounts of already-enriched molecular gas. The latter has sufficient density to be excited in the high-level rotational CO lines, which yield more flux than low-level lines, making easier high-redshift detections; however there is no negative K-correction as for the sub-millimeter and far-infrared dust continuum emission. With the help of simple galaxy models, based on these first detections, we estimate the flux in all CO lines expected for such starbursting objects at various redshifts. We discuss the detection perspectives with the future millimeter instruments