  Modern (sub-)millimeter interferometers enable the measurement of the cool
gas and dust emission of high-redshift galaxies (z>5). However, at these
redshifts the cosmic microwave background (CMB) temperature is higher,
approaching, and even exceeding, the temperature of cold dust and molecular gas
observed in the local Universe. In this paper, we discuss the impact of the
warmer CMB on (sub-)millimeter observations of high-redshift galaxies. The CMB
affects the observed (sub-)millimeter dust continuum and the line emission
(e.g. carbon monoxide, CO) in two ways: (i) it provides an additional source of
(both dust and gas) heating; and (ii) it is a non-negligible background against
which the line and continuum emission are measured. We show that these two
competing processes affect the way we interpret the dust and gas properties of
high-redshift galaxies using spectral energy distribution models. We quantify
these effects and provide correction factors to compute what fraction of the
intrinsic dust (and line) emission can be detected against the CMB as a
function of frequency, redshift and temperature. We discuss implications on the
derived properties of high-redshift galaxies from (sub-)millimeter data.
Specifically, the inferred dust and molecular gas masses can be severely
underestimated for cold systems if the impact of the CMB is not properly taken
into account.
