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.

Doctor of Philosophy / Department of Physics / Bharat Ratra / The last decade of the 20th century was marked by the discovery of the accelerated expansion of the universe. This discovery puzzles physicists and has yet to be fully understood. It contradicts the conventional theory of gravity, i.e. Einstein’s General Relativity (GR). According to GR, a universe filled with dark matter and ordinary matter, i.e. baryons, leptons, and photons, can only expand with deceleration. Two approaches have been developed to study this phenomenon. One attempt is to assume that GR might not be the correct description of gravity, hence a modified theory of gravity has to be developed to account for the observed acceleration of the universe’s expansion. This approach is known as the ”Modified Gravity Theory”. The other way is to assume that the energy budget of the universe has one more component which causes expansion of space with acceleration on large scales. Dark Energy (DE) was introduced as a hypothetical type of energy homogeneously filling the entire universe and very weakly or not at all interacting with ordinary and dark matter. Observational data suggest that if DE is assumed then its contribution to the energy budget of the universe at the current epoch should be about 70% of the total energy density of the universe. In the standard cosmological model a DE term is introduced into the Einstein GR equations through the cosmological constant, a constant in time and space, and proportional to the metric tensor g[subscript]mu[subscript]nu. While this model so far fits most available observational data, it has some significant conceptual shortcomings. Hence there are a number of alternative cosmological models of DE in which the dark energy density is allowed to vary in time and space.

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).

Doctor of Philosophy / Department of Physics / Uwe Thumm / We study the dynamics of diatomic molecules (dimers) in intense IR and XUV laser fields theoretically and compare the results with measured data in collaboration with different experimental groups worldwide. The first three chapters of the thesis cover the introduction and the background on solving time-independent and time-dependent Schrödinger equation. The numerical results in this thesis are presented in four chapters, three of which are focused on diatomic molecules in IR fields. The last one concentrates on diatomic molecules in XUV pulses. The study of nuclear dynamics of H[subscript]2 or D[subscript]2 molecules in IR pulses is given in Chapter 4. First, we investigate the optimal laser parameters for observing field-induced bond softening and bond hardening in D[subscript]2[superscript]+. Next, the nuclear dynamics of H[subscript]2[superscript]+ molecular ions in intense laser fields are investigated by analyzing their fragment kinetic-energy release (KER) spectra as a function of the pump-probe delay τ. Lastly, the electron localization is studied for long circularly polarized laser pulses. Chapter 5 covers the dissociation dynamics of O[subscript]2[superscript]+ in an IR laser field. The fragment KER spectra are analyzed as a function of the pump-probe delay τ. Within the Born-Oppenheimer approximation, we calculate ab-initio adiabatic potential-energy curves and their electric dipole couplings, using the quantum chemistry code GAMESS. In Chapter 6, the dissociation dynamics of the noble gas dimer ions He[subscript]2[superscript]+, Ne[subscript]2[superscript]+, Ar[subscript]2[superscript]+, Kr[subscript]2[superscript]+, and Xe[subscript]2[superscript]+ is investigated in ultrashort pump and probe laser pulses of different wavelengths. We observe a striking ‘‘delay gap’’ in the pump-probe-delay-dependent KER spectrum only if the probe-pulse wavelength exceeds the pump-pulse wavelength. Comparing pump-probe-pulse-delay dependent KER spectra for different noble gas dimer cations, we quantitatively discuss quantum-mechanical versus classical aspects of the nuclear vibrational motion as a function of the nuclear mass. Chapter 7 focuses on diatomic molecules in XUV laser pulses. We trace the femtosecond nuclear-wave-packet dynamics in ionic states of oxygen and nitrogen diatomic molecules by comparing measured kinetic-energy-release spectra with classical and quantum-mechanical simulations. Experiments were done at the free-electron laser in Hamburg (FLASH) using 38-eV XUV-pump–XUV-probe. The summary and outlook of the work is discussed in Chapter 8.