Probing The Cosmological Constant Through The Alcock-Paczynski Test   Based on The Lyman-Alpha Forest
  In recent years, the possibility of measuring the cosmological constant $\Omega_\Lambda$ through the application of the Alcock-Paczynski test to the Lyman Alpha (Ly$\alpha$) forest has been suggested (McDonald et al. 1999; Hui et al. 1999). Despite the theoretical uncertainties due to a few other cosmological parameters, some of the greatest difficulties we encounter concern the huge uncertainties due to cosmic variance and noise. In this paper, we propose a maximum likelihood estimation (MLE) method to deal with cosmic variance and noise using synthetic spectra of quasistellar objects (QSOs) from our cosmological hydrodynamic simulations. We demonstrate that the MLE method can overcome the cosmic variance problem. Applying the MLE method, we find that we have more than 90% probability to determine $\Omega_\Lambda$ within 20% error and approximately of 66% probability to determine $\Omega_\Lambda$ within 10% error by using 30 pairs QSO spectra when other cosmological parameters are assumed. Another important source of error is from noise in the flux spectra, and we have modeled the corresponding effect by studying artificial spectra with different kinds of noise added. We discover that the noise distribution does not have significant effect on the final cross-correlation functions as long as the signal-to-noise ratio (S/N) is fixed. Finally, a preliminary test and discussion about the sensitivities to other cosmological parameters are included in this paper as well. 
Wen-Ching Lin and Michael Norman