Master of Science / Department of Physics / Bharat Ratra / Recent observations in cosmology suggest that the universe is undergoing accelerating expansion. Mysterious component responsible for acceleration is called "Dark Energy" contributing to 70% of total energy density of the universe. Simplest DE model is [Lambda]CDM, where Einstein’s cosmological constant plays role of the dark energy. Despite the fact that it is consistent with observational data, it leaves some important theoretical questions unanswered. To overcome these difficulties different Dark energy models are proposed. Two of these models XCDM parametrization and slow rolling scalar field model [phi]CDM, along with "standard" [Lambda]CDM are disscussed here, constraining their parameter set. In this thesis we start with a general theoretical overview of basic ideas and distance measures in cosmology. In the following chapters we use H II starburst galaxy apparent magnitude versus redshift data from Siegel et al.(2005) to constrain DE model parameters. These constraints are generally consistent with those derived using other data sets, but are not as restrictive as the tightest currently available constraints. Also we constrain above mentioned cosmological models in light of 32 age measurements of passively evolving galaxies as a function of redshift and recent estimates of the product of the cosmic microwave background acoustic scale and the baryon acoustic oscillation peak scale.

Doctor of Philosophy / Department of Physics / Bharat Ratra / The expansion rate of the Universe changes with time, initially slowing (decelerating) when the universe was matter dominated, because of the mutual gravitational attraction of all the matter in it, and more recently speeding up (accelerating). A number of cosmological observations now strongly support the idea that the Universe is spatially flat (provided the dark energy density is at least approximately time independent) and is currently undergoing an accelerated cosmological expansion. A majority of cosmologists consider ``dark energy" to be the cause of this observed accelerated cosmological expansion. The ``standard" model of cosmology is the spatially-flat $\Lambda$CDM model. Although most predictions of the $\Lambda$CDM model are reasonably consistent with measurements, the $\Lambda$CDM model has some curious features. To overcome these difficulties, different Dark Energy models have been proposed. Two of these models, the XCDM parametrization and the slow rolling scalar field model $\phi$CDM, along with ``standard" $\Lambda$CDM, with the generalization of XCDM and $\phi$CDM in non-flat spatial geometries are considered here and observational data are used to constrain their parameter sets. In this thesis, we start with a overview of the general theory of relativity, Friedmann's equations, and distance measures in cosmology. In the following chapters we explain how we can constrain the three above mentioned cosmological models using three data sets: measurements of the Hubble parameter $H(z)$, Supernova (SN) apparent magnitudes, and the baryonic acoustic oscillations (BAO) peak length scale, as functions of redshift $z$. We then discuss constraints on the deceleration-acceleration transition redshift $z_{\rm da}$ using unbinned and binned $H(z)$ data. Finally, we incorporate the spatial curvature in the XCDM and $\phi$CDM model and determine observational constraints on the parameters of these expanded models.

Master of Science / Department of Physics / Bharat Ratra / In this report, we discuss the four standard energy conditions of General Relativity (null, weak, dominant, and strong) and investigate their cosmological consequences. We note that these energy conditions can be compatible with cosmic acceleration provided that a repulsive cosmological constant exists and the acceleration stays within certain bounds. Scalar fields and dark energy, and their relationships to the energy conditions, are also discussed. Special attention is paid to the 1988 Ratra-Peebles scalar field model, which is notable in that it provides a physical self-consistent framework for the phenomenology of dark energy. Appendix B, which is part of joint-research with Anatoly Pavlov, Khaled Saaidi, and Bharat Ratra, reports on the existence of the Ratra-Peebles scalar field tracker solution in a curvature-dominated universe, and discusses the problem of investigating the evolution of long-wavelength inhomogeneities in this solution while taking into account the gravitational back-reaction (in the linear perturbative approximation).