Lyman alpha absorbers in motion: consequences of gravitational lensing
  for the cosmological redshift drift experiment
  The evolution of the expansion rate of the Universe results in a drift in the
redshift of distant sources over time. A measurement of this drift would
provide us with a direct probe of expansion history. The Lyman alpha forest has
been recognized as the best candidate for this experiment, but the signal would
be weak and it will take next generation large telescopes coupled with
ultra-stable high resolution spectrographs to reach the cm/s resolution
required. One source of noise that has not yet been assessed is the transverse
motion of Lyman alpha absorbers, which varies the gravitational potential in
the line of sight and subsequently shifts the positions of background
absorption lines. We examine the relationship between the pure cosmic signal
and the observed redshift drift in the presence of moving Lyman alpha clouds,
particularly the collapsed structures associated with Lyman limit systems
(LLSs) and damped Lyman alpha systems (DLAs). Surprisingly, the peculiar
velocities and peculiar accelerations both enter the expression, although the
acceleration term stands alone as an absolute error, whilst the velocity term
appears as a fractional noise component. An estimate of the magnitude of the
noise reassures us that the motion of the Lyman alpha absorbers will not pose a
threat to the detection of the signal.
