Cosmological perturbation theory (CPT) is an important tool with which inhomogeneities that seed the observed structure of our universe can be studied. This thesis introduces the subject of CPT and discusses applications of this at both linear and second order. At linear order the evolution of the curvature perturbation around horizon crossing is examined. We study single field inflation models numerically, and compare the curvature perturbation at horizon crossing to that at the end of inflation. In addition, linear-order CPT is extended to the case of a multi-fluid system and an approximation for the velocities of the baryons and photons in the early universe as well as the strength of the electric field is found. We use second order CPT to study magnetogenesis. By using fully relativistic, non-linear CPT we show how magnetic fields are generated. This is done by presenting the first fully analytical calculation of the magnetic field at second order. Our results suggest that magnetic fields with strengths of the order of 10²⁷G and with scale dependence M ∝ k⁴ may be generated - findings which are largely in agreement with previous numerical results. We end by outlining possible extensions to this work, in particular related to the study of primordial magnetogenesis.

According to current cosmological theory, the rate of expansion of the universe depends on the average energy densities of matter, radiation, and a possible vacuum energy described by a cosmological constant, &Lambda;, in the Einstein equation.<p>Observations of galaxies and radiation, along with an assumption that we hold no special place in the universe, imply an isotropic and homogeneous energy distribution, for which the universal rate of expansion for most of the history of the universe may be constructed to depend only on present values of the dimensionless matter and vacuum energy density parameters, &Omega;_M and &Omega;_&Lambda;, respectively, and the present rate of expansion of the universe, H₀. Over the past decade, much progress has been made in determining the values of the three density parameters using a variety of independent methods. In particular, observations of type Ia supernovae in the late 1990s provided the first evidence that &Lambda; &ne; 0 and that universal expansion is accelerating.<p>This study has determined values for &Omega;_M and &Omega;_&Lambda; using the brightest quasars in the Sloan Digital Sky Survey Data Release 5, which are located at a range of distances - equivalently, a range of lookback times - that have not been accessible through any other observations. After fitting the apparent magnitudes of the brightest quasars at various redshifts to the distance modulus equation with a luminosity evolution term, values for the density parameters were determined to be &Omega;_M = 0.07 and &Omega;_&Lambda; = 1.13.

According to current cosmological theory, the rate of expansion of the universe depends on the average energy densities of matter, radiation, and a possible vacuum energy described by a cosmological constant, &Lambda;, in the Einstein equation.<p>Observations of galaxies and radiation, along with an assumption that we hold no special place in the universe, imply an isotropic and homogeneous energy distribution, for which the universal rate of expansion for most of the history of the universe may be constructed to depend only on present values of the dimensionless matter and vacuum energy density parameters, &Omega;_M and &Omega;_&Lambda;, respectively, and the present rate of expansion of the universe, H₀. Over the past decade, much progress has been made in determining the values of the three density parameters using a variety of independent methods. In particular, observations of type Ia supernovae in the late 1990s provided the first evidence that &Lambda; &ne; 0 and that universal expansion is accelerating.<p>This study has determined values for &Omega;_M and &Omega;_&Lambda; using the brightest quasars in the Sloan Digital Sky Survey Data Release 5, which are located at a range of distances - equivalently, a range of lookback times - that have not been accessible through any other observations. After fitting the apparent magnitudes of the brightest quasars at various redshifts to the distance modulus equation with a luminosity evolution term, values for the density parameters were determined to be &Omega;_M = 0.07 and &Omega;_&Lambda; = 1.13.

<p> Hawking's Singularity Theorem establishes the existence of a cosmological singularity in a spacetime for which no global assumptions about causality are made. This theory has been useful for predicting the occurrence of singularities in a spacetime without solving Einstein's field equation. This paper is an exposition of the tools and some of the theory required to prove and apply Hawking's theorem. Emphasis is placed on practical methods for applying this result to the flat, dust-filled Robertson-Walker spacetime, and the black hole interior of the Kruskal extension of the Schwarzschild spacetime.</p> / Thesis / Master of Science (MSc)

No description available.

In this thesis we review and build on the common methods used to analyze null geodesics in Schwarzschild de Sitter space. We present a general technique which allows finding measurable intersection angles of null trajectories analytically, and as one of its applications we establish a general relativistic aberration relationship. The tools presented are used to analyze some standard setups of gravitational deflection of light and gain a clear understanding of the role that the cosmological constant, Λ, plays in gravitational lensing phenomena. Through reviewing some recent papers on the topic with the present results in mind, we attempt to explain the major sources of disagreement in the ongoing debate on the subject, which started with Rindler and Ishak’s original paper, regarding the influence of Λ on lensing phenomena. To avoid ambiguities and room for misunderstanding we present clear definitions of the quantities used in the present analysis as well as in other papers we discuss. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-09-30 21:18:26.762

In this thesis we present research into linear perturbations in Lemaître-Tolman-Bondi (LTB) and Assisted Coupled Quintessence (ACQ) Cosmologies. First we give a brief overview of the standard model of cosmology. We then introduce Cosmological Perturbation Theory (CPT) at linear order for a at Friedmann-Robertson-Walker (FRW) cosmology. Next we study linear perturbations to a Lemaître-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities in LTB. We show, using the perturbed energy conservation equation, that there is a conserved quantitiy in LTB which is conserved on all scales. We then briefly extend our discussion to the Lemaître spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime. We also study the behaviour of linear perturbations in assisted coupled quintessence models in a FRW background. We provide the full set of governing equations for this class of models, and solve the system numerically. The code written for this purpose is then used to evolve growth functions for various models and parameter values, and we compare these both to the standard CDM model and to current and future observational bounds. We also examine the applicability of the "small scale approximation", often used to calculate growth functions in quintessence models, in light of upcoming experiments such as SKA and Euclid. We nd the results of the full equations deviates from the approximation by more than the experimental uncertainty for these future surveys. The construction of the numerical code, Pyessence, written in Python to solve the system of background and perturbed evolution equations for assisted coupled quintessence, is also discussed.

We propose and construct a two-parameter expansion around a Friedmann-Lemaitre- Robertson-Walker geometry which uses both large-scale and small-scale perturbations analogous to cosmological perturbation theory and post-Newtonian gravity. We justify this observationally, derive a set of field equations valid on a fraction of the horizon size and perform a detailed investigation of the associated gauge problem. We find only the Newtonian gauge, out of the standard gauges used in cosmological perturbation theory, is applicable to post-Newtonian perturbations; we can identify a consistent set of perturbed quantities in the matter and gravity sectors and construct corresponding gauge-invariant quantities. The field equations, written in terms of these quantities, takes on a simpler form, and allows the effects of small-scale structure on the large-scale properties of the Universe to be clearly identified and discussed for different physical scenarios. With a definition of statistical homogeneity, we find that the cosmological constant and the average energy density, of radiation and dust, source the Friedmann equation, whereas only the inhomogeneous part of the Newtonian energy density sources the Newton-Poisson equation { even though both originate from the same equation. There exists field equations at new orders in our formalism, such as a frame-dragging field equation a hundred times larger than expected from using cosmological perturbation theory alone. Moreover, we find non-linear gravity, mode-mixing and a mixing-of-scales at orders one would not expect from intuition based on cosmological perturbation theory. By recasting the field equations as an effective fluid we observe that these non-linearities lead to, for example, a large-scale effective pressure and anisotropic stress. We expect our formalism to be useful for accurately modelling our Universe, and for investigating the effects of non-linear gravity in the era of ultra-large-scale surveys.

The spin-foam is a covariant path-integral style approaching to the quantization of the gravity. There exist several spin-foam models of which the most successful one is the Engle-Pereira-Rovelli-Levine/Freidel-Krasnov (EPRL-FK) model. Using the EPRLFK model people are able to calculate the transition amplitude and the n-point functions of 4D geometry (both Euclidean and Lorentzian) surrounding by a given triangulated 3D geometry. The semi-classical limit of the EPRL-FK amplitude reproduces discrete classical gravity under certain assumptions, which shows that the EPRLFK model can be understood as UV completion of general relativity. On the other hand, it is very hard to dene a continuum limit and couple a cosmological constant to the EPRL-FK model. In this dissertation, we addressed the problems about continuum limit and coupling a cosmological constant to the EPRL-FK model. Followed by chapter one as a brief introduction of the loop quantum gravity and EPRL-FK model, chapter two introduces our work about demonstrating (for the first time) that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete spin-foam models under an appropriate low energy limit, which corresponds to a semi-classical continuum limit of spin-foam models. In chapter three, we bring in the cosmological constant into the spin-foam model by coupling the SL(2, C) Chern-Simons action with the EPRL action, and find that the quantum simplicity constraint is realized as the 2d surface defect in SL(2, C)Chern-Simons theory in the construction of spin-foam amplitudes. In chapter four, we present a way to describe the twisted geometry with cosmological constant whose corresponding quantum states can forms the Hilbert space of the loop quantum gravity with cosmological constant. In chapter five, we introduced a new definition of the graviton propagator, and calculate its semi-classical limit in the contents of spin-foam model with the cosmological constant. Finally the chapter six will be a outlook for my future work. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

No description available.