Fundamental physics with Espresso: Towards an accurate wavelength
  calibration for a precision test of the fine-structure constant
  Observations of metal absorption systems in the spectra of distant quasars
allow to constrain a possible variation of the fine-structure constant
throughout the history of the Universe. Such a test poses utmost demands on the
wavelength accuracy and previous studies were limited by systematics in the
spectrograph wavelength calibration. A substantial advance in the field is
therefore expected from the new ultra-stable high-resolution spectrograph
Espresso, recently installed at the VLT. In preparation of the fundamental
physics related part of the Espresso GTO program, we present a thorough
assessment of the Espresso wavelength accuracy and identify possible
systematics at each of the different steps involved in the wavelength
calibration process. Most importantly, we compare the default wavelength
solution, based on the combination of Thorium-Argon arc lamp spectra and a
Fabry-P\'erot interferometer, to the fully independent calibration obtained
from a laser frequency comb. We find wavelength-dependent discrepancies of up
to 24m/s. This substantially exceeds the photon noise and highlights the
presence of different sources of systematics, which we characterize in detail
as part of this study. Nevertheless, our study demonstrates the outstanding
accuracy of Espresso with respect to previously used spectrographs and we show
that constraints of a relative change of the fine-structure constant at the
$10^{-6}$ level can be obtained with Espresso without being limited by
wavelength calibration systematics.
