Probing variations in the fundamental constants with quasar absorption lines

Precision cosmology challenges many aspects of fundamental physics. In particular, quasar absorption lines test the assumed constancy of fundamental constants over cosmological time-scales and distances. Until recently, the most reliable technique was the alkali doublet (AD) method where the measured doublet separation probes variations in the fine-structure constant, \ (e²/ c\). However, the recently introduced many-multiplet (MM) method provides several advantages, including a demonstrated ≈10-fold precision gain. This thesis presents detailed MM analyses of 3 independent Keck/HIRES samples containing 128 absorption systems with \ (0. 2 < z ₀₁ₒ < 3. 7\). We find \ (5. 6\) statistical evidence for a smaller α in the absorption clouds: \ (/ = (-0. 574 0. 102) 10^-5\). All three samples separately yield consistent, significant \ (/\). The data marginally prefer constant \ (d/dt\) rather than constant \ (/\). The two-point correlation function for α and the angular distribution of \ (/\) give no evidence for spatial variations. We also analyse 21 Keck/HIRES Si iv doublets, obtaining a 3-fold relative precision gain over previous AD studies: \ (/ = (0. 5 1. 3) 10^-5\) for \ (2. 0 < z ₀₁ₒ < 3. 1\). Our statistical evidence for varying α requires careful consideration of systematic errors. Modelling demonstrates that atmospheric dispersion is potentially important. However, the quasar spectra suggest a negligible effect on \ (/\). Cosmological variation in Mg isotopic abundances may affect \ (/\) at \ (z ₀₁ₒ < 1. 8\). Galactic observations and theory suggest diminished 25, 26Mg abundances in the low metallicity quasar absorbers. Removing 25, 26Mg isotopes yields more negative \ (/\) values. Overall, known systematic errors can not explain our results. We also constrain variations in \ (y = ²g ₏\), comparing H I 21-cm and millimetre-wave molecular absorption in 2 systems. Fitting both the H I and molecular lines yields the tightest, most reliable current constraints: \ (y/y = (-0. 20 0. 44) 10^-5\) and \ (y/y = (-0. 16 0. 54) 10^-5\) at \ (z ₀₁ₒ = 0. 2467\) and 0. 6847 respectively. Possible line-of-sight velocity differences between the H I and molecular absorbing regions dominate these \ (1\) errors. A larger sample of mm/H I comparisons is required to reliably quantify this uncertainty and provide a potentially crucial check on the MM result.