Probing dark energy with theory and observations

The discovery of cosmic acceleration twelve years ago implies that our universe is dominated by dark energy, which is either a tiny cosmological constant or a mysterious fluid with large negative pressure, or that Einstein's successful theory of gravity needs to be modified at large scales/low energies. Since then, independent evidence of a number of cosmological probes has firmly established the picture of a universe where dark energy (or the effective contribution from a modification of gravity) makes up about 72% of the total energy density. Whichever of the options mentioned above will turn out to be the right one, a satisfying explanation for cosmic acceleration will likely lead to important new insights in fundamental physics. The question of the physics behind cosmic acceleration is thus one of the most intriguing open questions in modern physics. In this thesis, we calculate current constraints on dark energy and study how to optimally use the cosmological tools at our disposal to learn about its nature.;We will first present constraints from a host of recent data on the dark energy sound speed and equation of state for different dark energy models including early dark energy. We then study the observational properties of purely kinetic k-essence models and show how they can in principle be straightforwardly distinguished from quintessence models by their equation of state behavior. We next consider a large, representative set of dark energy and modified gravity models and show that they can be divided into a small set of observationally distinct classes. We also find that all non-early dark energy models we consider can be modeled extremely well by a simple linear equation of state form. We will then go on to discuss a number of alternative, model independent parametrizations of dark energy properties. Among other things, we find that principal component analysis is not as model-independent as one would like it to be and that assuming a fixed value for the high redshift equation of state can lead to a dangerous bias in the determination of the equation of state at low redshift. Finally, we discuss using weak gravitational lensing of cosmic microwave background (CMB) anisotropies as a cosmological probe. We compare different methods for extracting cosmological information from the lensed CMB and show that CMB lensing will in the future be a useful tool for constraining dark energy and neutrino mass. Whereas marginalizing over neutrino mass can degrade dark energy constraints, CMB lensing helps to break the degeneracy between the two and restores the dark energy constraints to the level of the fixed neutrino mass case.