The Hubble constant H0 is the rate of expansion of the universe today. The discrepancy between the early universe H0 value, inferred using ΛCDM from Planck observations of the CMB, and the late universe H0 value, obtained using luminosity and distance measurements from a Type Ia Supernova (SNIa) distance ladder, has now reached 4.2σ. Despite improvements in precision, this tension has increased. This thesis studies these two measurements, as well as various other H0 determinations, which are independent of both the CMB and the SNIa distance ladder and corroborate the Hubble tension (with the caveat that many have large uncertainties), with a particular focus on lensing and gravitational waves. Some of the very many solutions proposed to resolve the Hubble tension are also explored, with an emphasis on late universe solutions and Early Dark Energy. The improvement in precision, the growing discrepancy, and the supporting independent measurements of the Planck and SNIa distance ladder H0 values are strong evidence that a significant tension between the early and late universe exists. This indicates that some modification to or expansion of ΛCDM is required. A great deal of models and solutions have been proposed to do so, however none have managed to fully resolve the tension yet.
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Department of Mathematics and Applied Mathematics