In this thesis we present work done in an analysis of models of brane induced gravity. These are higher dimensional generalizations of Einstein's General relativity where our universe is considered as a brane in a higher dimensional bulk and where the gravitational dynamics on the brane is enhanced. This provides a modification of gravity on the brane as compared to ordinary general relativity, primarily at very large distances. These models are therefore very interesting for adressing the cosmological constant problem. Even though the basic setup is natural to consider from the perspective of effective field theory and also follow from certain string theoretical considerations, the models have been plagued by inconsistencies in the form of unstable modes. In particular, a ghostlike and tachyonic scalar mode appears already at the linear level in a perturbative treatment. In order to gain a deeper insight into the nature of these consistency problems we have revisited the models, performing a more extensive analysis of the generic models than has previously been done. We have worked entirely in a gauge invariant formalism in order not to be obscured by gauge issues. We have also incorporated an effective thickness of the brane in our analysis and performed an explicit analysis of the effect of contributions from the extrinsic geometry. Although our analysis has been carried out at the linear level in a perturbative treatment we are able to get a deeper understanding of the unstable mode and illuminate some of the difficulties of these models that would likely persist even in a full nonlinear analysis.

Thesis (Ph. D.)--University of Chicago, Department of Astronomy & Astrophysics, August 2001. / Includes bibliographical references. Also available on the Internet.

We consider a recent approach to the construction of gauge-invariant relational observables in gravity in the context of cosmological perturbation theory. These observables are constructed using a field-dependent coordinate system, which we take to be geodesic lightcone coordinates. We show that the observables are gauge-independent in the fully nonlinear theory, and that they have the expected form when one adopts the geodesic lightcone gauge for the metric. We give explicit expressions for the Sasaki-Mukhanov variable at linear order, and the Hubble rate — as measured both by geodesic observers and by observers co-moving with the inflaton — to second order. Moreover, we show that the well-known linearised equations of motion for the Sasaki-Mukhanov variable and the scalar constraint variables follow from the gauge-invariant Einstein’s equations

Doctor of Philosophy / Department of Physics / Bharat Ratra / High precision cosmological observations in last decade suggest that about 70% of our universe's energy density is in so called "Dark Energy" (DE). Observations show that DE has negative effective pressure and therefore unlike conventional energy sources accelerates the cosmic expansion instead of decelerating it. DE is highly uniform and has become a dominant component only recently. The simplest candidate for DE is the time-independent cosmological constant. Although successful in fitting available data, the cosmological constant model has a number of theoretical shortcomings and because of that alternative models of DE are considered. In one such scenario a cosmological scalar field that slowly rolls down its potential acts like a time-dependent cosmological constant. I have used different independent cosmological data sets to constrain the time dependence of DE's energy density in the framework of the slowly-rolling cosmological scalar field model. Present data favors a time-independent cosmological constant, but the time-dependent DE can not be ruled out at high confidence level. Ongoing and planned cosmological probes and surveys will provide more and better quality data over the next decade. When the new data sets are available we will be able to either detect the time dependence of DE or constrain it to a very small physically uninteresting value.

One of the exciting aspects of cosmology is to understand the period of `cosmic inflation' that powered the epoch of the Big Bang. Inflation has been very successful in explaining several puzzles of the standard big bang scenario. But the most important success of inflation is that it can explain the temperature fluctuations of cosmic microwave background and the large scale structures of the universe. Despite its great success, the details of the physics of inflation are still unknown. A large number of models of inflation successfully explain all the observations making it remarkably hard to distinguish between different models. We explore the possibility of differentiating between different inflationary models by studying two-point and three-point functions of primordial fluctuations produced during inflation. First, we explore possible constraints on the inflationary equation state by considering current measurements of the power spectrum. Next, we explore the possibility of a single field slow-roll inflationary model with general initial state for primordial fluctuations. The two-point and three-point functions of primordial fluctuations are generally computed assuming that the fluctuations are initially in the Bunch-Davies state. However, we show that the constraints on the initial state from observed power spectrum and local bispectrum are relatively weak and for slow-roll inflation a large number of initial states are consistent with the current observations. As the precision of the observations is increasing significantly, we may learn more about the initial state of the fluctuations in the near future. Finally, we explore the consistency relations for the three-point functions, in the squeezed limit, of scalar and tensor perturbations in single-field inflation that in principle can be used to differentiate between single-field and multi-field inflation models. However, for slow-roll inflation, we find that it is possible to violate some of the consistency relations for initial states that are related to the Bunch-Davies state by Bogoliubov transformations and we identify the reason for the violation. Then we discuss the observational implications of this violation. / text

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My overall claim in this paper is twofold: Firstly, the activity of developing arguments in favour of the existence of the Christian God is tenable and worthwhile and, secondly, the “infinite God objection” fails to undermine the kalam cosmological argument. Concerning the former, it is often claimed that the very activity of developing arguments in favour of God’s existence is futile. I argue, however, that such theistic arguments play an important role in the philosophy of religion, natural theology, and apologetics. Concerning the latter claim, I will attempt to show how the infinite God objection fails to undermine a notable theistic argument, namely, the kalam cosmological argument. As regards this objection, the proponents of the kalam cosmological argument face a dilemma – either an actual infinity cannot exist or God’s knowledge cannot be infinite. More specifically, this objection claims that God’s omniscience entails the existence of an actual infinity with God knowing an actual infinite number of future events and mathematical truths. My solution to this problem is that (1) God’s omniscience should be understood as maximal knowledge; (2) the existence of abstract objects (such as numbers and propositions) should be denied; and (3) God’s knowledge is non-propositional in nature. / MPhil, North-West University, Potchefstroom Campus, 2014

The redshift drift of objects moving in the Hubble flow has been proposed as a powerful model-independent probe of the underlying cosmology. A measurement of the first- and second-order redshift derivatives appears to be well within the reach of upcoming surveys using as the Extremely Large Telescope high resolution spectrometer (ELT-HIRES) and the Square Kilometer Phase 2 Array (SKA). Here we show that an unambiguous prediction of the R-h = ct cosmology is zero drift at all redshifts, contrasting sharply with all other models in which the expansion rate is variable. For example, multiyear monitoring of sources at redshift z = 5 with the ELT-HIRES is expected to show a velocity shift Delta v = -15 cm s(-1) yr(-1) due to the redshift drift in Planck I > CDM, while Delta v = 0 cm s(-1) yr(-1) in R-h = ct. With an anticipated ELT-HIRES measurement error of +/- 5 cm s(-1) yr(-1) after 5 yr, these upcoming redshift drift measurements might therefore be able to differentiate between R-h = ct and Planck I > CDM at similar to 3 sigma, assuming that any possible source evolution is well understood. Such a result would provide the strongest evidence yet in favour of the R-h = ct cosmology. With a 20-yr baseline, these observations could favour one of these models over the other at better than 5 sigma.

Many physical theories beyond the Standard Model predict time variations of basic physics parameters. Direct measurement of the time variations of these parameters is very difficult or impossible to achieve. By contrast, measurements of fundamental constants are relatively easy to achieve, both in the laboratory and by astronomical spectra of atoms and molecules in the early universe. In this work, measurements of the proton to electron mass ratio mu and the fine structure constant alpha are combined to place mildly model-dependent limits on the fractional variation of the quantum chromodynamic scale and the sum of the fractional variations of the Higgs vacuum expectation value (VEV) and the Yukawa couplings on time-scales of more than half the age of the universe. The addition of another model parameter allows the fractional variation of the Higgs VEV and the Yukawa couplings to be computed separately. Limits on their variation are found at the level of less than 5 x 10(-5) over the past 7 Gyr. A model-dependent relation between the expected fractional variation of a relative to mu tightens the limits to 10(-7) over the same time span. Limits on the present day rate of change of the constants and parameters are then calculated using slow roll quintessence. A primary result of this work is that studies of the dimensionless fundamental constants such as a and mu, whose values depend on the values of the physics parameters, are excellent monitors of the limits on the time variation of these parameters.

Matter near a gravitational lens galaxy or projected along the line of sight (LOS) can affect strong lensing observables by more than contemporary measurement errors. We simulate lens fields with realistic threedimensional mass configurations (self-consistently including voids), and then fit mock lensing observables with increasingly complex lens models to quantify biases and uncertainties associated with different ways of treating the lens environment (ENV) and LOS. We identify the combination of mass, projected offset, and redshift that determines the importance of a perturbing galaxy for lensing. Foreground structures have a stronger effect on the lens potential than background structures, due to nonlinear effects in the foreground and downweighting in the background. There is dramatic variation in the net strength of ENV/LOS effects across different lens fields; modeling fields individually yields stronger priors for H-0 than ray tracing through N-body simulations. Models that ignore mass outside the lens yield poor fits and biased results. Adding external shear can account for tidal stretching from galaxies at redshifts z >= z(lens), but it requires corrections for external convergence and cannot reproduce nonlinear effects from foreground galaxies. Using the tidal approximation is reasonable for most perturbers as long as nonlinear redshift effects are included. Even then, the scatter in H0 is limited by the lens profile degeneracy. Asymmetric image configurations produced by highly elliptical lens galaxies are less sensitive to the lens profile degeneracy, so they offer appealing targets for precision lensing analyses in future surveys like LSST and Euclid.