Effect of model-dependent covariance matrix for studying Baryon Acoustic
  Oscillations
  Large-scale structures in the Universe are a powerful tool to test
cosmological models and constrain cosmological parameters. A particular feature
of interest comes from Baryon Acoustic Oscillations (BAOs), which are sound
waves traveling in the hot plasma of the early Universe that stopped at the
recombination time. This feature can be observed as a localized bump in the
correlation function at the scale of the sound horizon $r_s$. As such, it
provides a standard ruler and a lot of constraining power in the correlation
function analysis of galaxy surveys. Moreover the detection of BAOs at the
expected scale gives a strong support to cosmological models. Both of these
studies (BAO detection and parameter constraints) rely on a statistical
modeling of the measured correlation function $\hat{\xi}$. Usually $\hat{\xi}$
is assumed to be gaussian, with a mean $\xi_\theta$ depending on the
cosmological model and a covariance matrix $C$ generally approximated as a
constant (i.e. independent of the model). In this article we study whether a
realistic model-dependent $C_\theta$ changes the results of cosmological
parameter constraints compared to the approximation of a constant covariance
matrix $C$. For this purpose, we use a new procedure to generate lognormal
realizations of the Luminous Red Galaxies sample of the Sloan Digital Sky
Survey Data Release 7 to obtain a model-dependent $C_\theta$ in a reasonable
time. The approximation of $C_\theta$ as a constant creates small changes in
the cosmological parameter constraints on our sample. We quantify this modeling
error using a lot of simulations and find that it only has a marginal influence
on cosmological parameter constraints for current and next-generation galaxy
surveys. It can be approximately taken into account by extending the $1\sigma$
intervals by a factor $\approx 1.3$.
