Using quasar and gamma-ray burst measurements to constrain cosmological
  dark energy models
  Observational evidence for the accelerated expansion of the universe requires
dark energy for its explanation if general relativity is an accurate model of
gravity. However, dark energy is a mysterious quantity and we do not know much
about its nature so understanding dark energy is an exciting scientific
challenge. Cosmological dark energy models are fairly well tested in the low
and high redshift parts of the universe. The highest of the low redshift,
$z\sim2.3$, region is probed by baryon acoustic oscillation (BAO) measurements
and the only high redshift probe is the cosmic microwave background anisotropy
which probes the $z\sim1100$ part of redshift space. In the intermediate
redshift range $2.3 < z < 1100$ there are only a handful of observational
probes and cosmological models are poorly tested in this region.
  In this thesis we constrain three pairs of general relativistic cosmological
dark energy models using observational data which reach beyond the current BAO
limit. We use quasar X-ray and UV flux measurements, the current version of
these data span $0.009 \leq z \leq 7.5413$. We have discovered that most of
these data cannot be standardized using the proposed method. However, the lower
redshift part, $z \lesssim 1.5-1.7$, of these data are standardizable and can
be used to derive lower-$z$ cosmological constraints. Another data set we use
are gamma-ray burst measurements which span $0.3399 \leq z \leq 8.2$.
Cosmological constraints derived from these data are significantly weaker than,
but consistent with, those obtained from better-established cosmological
probes. We also study and standardize 78 reverberation-measured Mg II time-lag
quasars in the redshift range $0.0033 \leq z \leq 1.89$ by using their
radius-luminosity relation. We also study 118 reverberation-measured H$\beta$
time-lag quasars which span $0.0023 \leq z \leq 0.89$.
