The sensitivity of BAO Dark Energy Constraints to General Isocurvature
  Perturbations
  Baryon Acoustic Oscillation (BAO) surveys will be a leading method for
addressing the dark energy challenge in the next decade. We explore in detail
the effect of allowing for small amplitude admixtures of general isocurvature
perturbations in addition to the dominant adiabatic mode. We find that
non-adiabatic initial conditions leave the sound speed unchanged but instead
excite different harmonics. These harmonics couple differently to Silk damping,
altering the form and evolution of acoustic waves in the baryon-photon fluid
prior to decoupling. This modifies not only the scale on which the sound waves
imprint onto the baryon distribution, which is used as the standard ruler in
BAO surveys, but also the shape, width and height of the BAO peak. We discuss
these effects in detail and show how more general initial conditions impact our
interpretation of cosmological data in dark energy studies. We find that the
inclusion of these additional isocurvature modes leads to an increase in the
Dark Energy Task Force Figure of merit by 140% and 60% for the BOSS and ADEPT
experiments respectively when considered in conjunction with Planck data. We
also show that the incorrect assumption of adiabaticity has the potential to
bias our estimates of the dark energy parameters by $3\sigma$ ($1\sigma$) for a
single correlated isocurvature mode, and up to $8\sigma$ ($3\sigma$) for three
correlated isocurvature modes in the case of the BOSS (ADEPT) experiment. We
find that the use of the large scale structure data in conjunction with CMB
data improves our ability to measure the contributions of different modes to
the initial conditions by as much as 100% for certain modes in the fully
correlated case.
