The relationship between magnetism and superconductivity has become a central topic of research in studies of superconductivity in the iron pnictides. This thesis presents inelastic neutron scattering studies of the magnetic excitations in FeAs flux-grown CaFe₂As₂. The ex- perimental data collected using ARCS time-of-flight chopper spectrometer have been analyzed and compared with theoretical models. The focus here is on the role played by antiferromag- netic (AFM) spin fluctuations in superconductivity. We present unambiguous evidence of the absence of magnetic fluctuations in the non-superconducting volume collapsed tetragonal (cT) phase of CaFe₂As₂ via inelastic neutron scattering time-of-flight data, which is consistent with the view that spin fluctuations are a necessary ingredient for unconventional superconductivity in the iron pnictides. We demonstrate that the cT phase of CaFe₂As₂ is non-magnetic, raising new questions regarding recent reports of high-temperature superconductivity in the cT phase of closely related compounds.