| An important topic in cosmology is the determination of the energy densities of the major components of the Universe—ΩB, Ω DM and ΩΛ. Among these, the cosmological constant ΩΛ, which associates with the vacuum energy of our universe, draws specific attentions for its importance in fundamental particle physics. The Lyα forest QSO spectra are observationally available from z ∼ 0 to z ∼ 4. Recently the concept of performing the Alcock-Paczynski test on the Lyα forest to determine the cosmological constant has been proposed. This motivates us to develop a methodology incorporating sophisticated cosmological hydrodynamics simulations including these effects to implement the AP test and to perform an accurate measurement on the cosmological constant Ω Λ. To manipulate the data from paired QSO spectra with different angular separations, we propose an explicit method based on the maximum likelihood estimation. We use this method to implement the AP test and demonstrate the whole procedure based on our numerical simulations. Using mock pair spectra, we estimate that more than 40 pairs are required to derive an accurate value of ΩΛ due to the impact of cosmic variance. The degeneracy of other cosmological parameters is an important topic for this project. We examine two other parameters, σ8 and n, the initial power spectrum amplitude and index, whose value are not consistently derived through other means. We conclude that when the uncertainties of these two parameters are around 10%–20%, the resulting bias in Ω Λ is less than 10%. Using a small sample of currently available QSO pairs, we have derived ΩΛ = . Our preliminary result encourges us to take further steps on this project. |
