Dark matter has been shown to be extremely abundant in our universe. It comprises about 23 percent of the energy density of the entire universe, which is more than five times greater than the regular matter we already know about. Dark matter cannot be explained within the Standard Model of particle physics. However, models which extend the Standard Model, such as supersymmetry, can explain dark matter. This dissertation investigates the signals of some supersymmetry models in the context of collider physics. If dark matter particles or other supersymmetry particles are produced at some collider experiment, such as the Large Hadron Collider, it is important to know how we can find and measure the signatures and properties of these particles. This dissertation provides some measurement techniques for that exact purpose. These measurement techniques are also very general, making them useful for examining other models of particle physics as well. Lastly, if the supersymmetry model can be understood well enough from collider data, the connection back to cosmology can be made. Namely, it is possible to determine (from LHC data and using a standard cosmological calculation) the abundance of dark matter in the universe. Comparing this collider value with the value already measured will be a crucial step in understanding dark matter. This dissertation provides simulated results of this dark matter abundance calculation for a number of supersymmetry model points.

One of the primary targets of current and especially future cosmological observations are light thermal relics of the hot big bang. Within the Standard Model of particle physics, an important thermal relic are cosmic neutrinos, while many interesting extensions of the Standard Model predict new light particles which are even more weakly coupled to ordinary matter and therefore hard to detect in terrestrial experiments. On the other hand, these elusive particles may be produced efficiently in the early universe and their gravitational influence could be detectable in cosmological observables. In this thesis, we describe how measurements of the cosmic microwave background (CMB) and the large-scale structure (LSS) of the universe can shed new light on the properties of neutrinos and on the possible existence of other light relics. These cosmological observations are remarkably sensitive to the amount of radiation in the early universe, partly because free-streaming species such as neutrinos imprint a small phase shift in the baryon acoustic oscillations (BAO) which we study in detail in the CMB and LSS power spectra. Building on this analytic understanding, we provide further evidence for the cosmic neutrino background by independently confirming its free-streaming nature in different, currently available datasets. In particular, we propose and establish a new analysis of the BAO spectrum beyond its use as a standard ruler, resulting in the first measurement of this imprint of neutrinos in the clustering of galaxies. Future cosmological surveys, such as the next generation of CMB experiments (CMB-S4), have the potential to measure the energy density of relativistic species at the sub-percent level and will therefore be capable of probing physics beyond the Standard Model. We demonstrate how this improvement in sensitivity can indeed be achieved and present an observational target which would allow the detection of any extra light particle that has ever been in thermal equilibrium. Interestingly, even the absence of a detection would result in new insights by providing constraints on the couplings to the Standard Model. As an example, we show that existing bounds on additional scalar particles, such as axions, may be surpassed by orders of magnitude.