  In an effort to resolve the discrepancy between two measurements of the
fundamental constant mu, the proton to electron mass ratio, at early times in
the universe we reanalyze the same data used in the earlier studies. Our
analysis of the molecular hydrogen absorption lines in archival VLT/UVES
spectra of the damped Lyman alpha systems in the QSOs Q0347-383 and Q0405-443
yields a combined measurement of a (Delta mu)/mu value of (-7 +/- 8) x 10^{-6},
consistent with no change in the value of mu over a time span of 11.5
gigayears. Here we define (Delta mu) as (mu_z - mu_0) where mu_z is the value
of mu at a redshift of z and mu_0 is the present day value. Our null result is
consistent with the recent measurements of King et al. 2009, (Delta mu)/u =
(2.6 +/- 3.0) x 10^{-6}, and inconsistent with the positive detection of a
change in mu by Reinhold et al. 2006. Both of the previous studies and this
study are based on the same data but with differing analysis methods.
Improvements in the wavelength calibration over the UVES pipeline calibration
is a key element in both of the null results. This leads to the conclusion that
the fundamental constant mu is unchanged to an accuracy of 10^{-5} over the
last 80% of the age of the universe, well into the matter dominated epoch. This
limit provides constraints on models of dark energy that invoke rolling scalar
fields and also limits the parameter space of Super Symmetric or string theory
models of physics. New instruments, both planned and under construction, will
provide opportunities to greatly improve the accuracy of these measurements.
