Dark energy is the as yet unidentified mechanism responsible for the accelerated expansion of the universe. Understanding this mechanism is one of the most important problems in modern cosmology for two reasons. First, dark energy is estimated to be responsible for approximately 70% of the energy content in the Universe, which means that we cannot have a complete model for the evolution of the structure in the Universe without understanding dark energy. Second, the current Standard Model of physics does not provide an explanation for dark energy. This means that understanding dark energy could serve as a gateway to physics beyond the current Standard Model.
The onus of constraining dark energy falls on observations. Since dark energy affects the expansion of the Universe, studying the behavior of dark energy currently requires the use of observables sensitive to the expansion. These include Type Ia supernovae, baryon acoustic oscillations, the anisotropies in the cosmic microwave background, and weak gravitational lensing. However, at present, the constraints provided by these probes are still rather weak. This leaves the pool of viable dark energy models quite large. There are two ways to alleviate this problem: the first is to acquire more data from those observational probes that are already employed, and the second is to develop complimentary observational probes.
In this thesis I take the latter approach by exploring the use of the Lyman alpha Forest as a probe of dark energy. In particular, I have investigated whether time-dependent dark energy leaves an observationally detectable signature in the flux power spectrum of the Lyman alpha Forest.
To this end, I have run five high-resolution, large-scale cosmological simulations using a modified version of the publicly available smoothed-particle hydrodynamics code GADGET-2. Each simulation employed a different dark energy model. Four of these dark energy models are dynamical models while the fifth is the standard cosmological constant, or vacuum energy. I then developed efficient massively-parallel codes in order to extract both synthetic Lyman alpha Forest spectra and synthetic flux power spectra from my simulations.
These power spectra were then compared against one another using the k-sample Anderson-Darling test. The results of these tests indicate that there is insufficient statistical distinction between the power spectra calculated from my dynamical dark energy simulations and the power spectra calculated from a cosmological constant simulation (0.05 significance level). The effects of my chosen dark energy models on the power spectrum are so small as to suggest that there is likely no prospect of future observations being able to distinguish between power spectra from different dark energy models. This implies that other approaches to the Lyman alpha Forest must be explored to find a significant signature of the time-dependent dark energy.