The density, the cosmic microwave background, and the proton-to-electron
  mass ratio in a cloud at redshift 0.9
  Based on measurements with the Effelsberg 100-m telescope, a multi-line study
of molecular species is presented toward the gravitational lens system
PKS1830-211. Obtaining average radial velocities and performing Large Velocity
Gradient radiative transfer calculations, the aims of this study are (1) to
determine the density of the gas, (2) to constrain the temperature of the
cosmic microwave background, and (3) to evaluate the proton-to-electron mass
ratio at redshift 0.9. Analyzing data from six rotational HC3N transitions
(this includes the J=7-6 line, which is likely detected for the first time in
the interstellar medium) we obtain about 2000 cm-3 for the gas density of the
south-western absorption component. Again toward the south-western source,
excitation temperatures of molecular species with optically thin lines and
higher rotational constants are, on average, consistent with the expected
temperature of the cosmic microwave background, T_CMB = 5.14 K. However,
individually, there is a surprisingly large scatter which far surpasses
expected uncertainties. A comparison of CS J=1-0 and 4-3 optical depths toward
the weaker north-western absorption component results in an excitation
temperature of 11 K and a 1-sigma error of 3 K. For the south-eastern main
component, a comparison of velocities determined from ten optically thin NH3
inversion lines with those from five optically thin rotational transitions of
HC3N, observed at similar frequencies, constrains potential variations of the
proton-to-electron mass ratio, with respect to its present value, to <1.4 x
10^-6 with 3-sigma confidence. Also including optically thin rotational lines
from other molecular species, it is emphasized that systematic errors are
smaller than 1 km/s, corresponding to an uncertainty of 10-6.
