Search for cosmological mu variation from high redshift H2 absorption; a
  status report
  Observations of H2 spectra in the line-of-sight of distant quasars may reveal
a variation of the proton-electron mass ratio mu=m_p/m_e at high redshift,
typically for z>2. Currently four high-quality systems (Q0347-383, Q0405-443,
Q0528-250 and J2123-005) have been analyzed returning a constraint Dmu/mu < 1 x
10^{-5}. We present data and a mu-variation analysis of another system,
Q2348-011 at redshift z_{abs}=2.42, delivering dmu/mu = (-1.5 \pm 1.6) x
10^{-5}. In addition to observational data the status of the laboratory
measurements is reviewed. The future possibilities of deriving a competitive
constraint on Dmu/mu from the known high-redshift H2 absorbers is investigated,
resulting in the identification of a number of potentially useful systems for
detecting mu-variation.
