Streaming motions of galaxies and clusters provide the only method for probing the distribution of mass, as opposed to light, on scales of 20 - 100 h(^-1)Mpc. This thesis presents a new survey of the local peculiar velocity field, based upon Fundamental Plane (FP) distances for an all-sky sample of 56 clusters to cz = 12000 km s(^-1). Central velocity dispersions have been determined from new spectroscopic data for 429 galaxies. From new R-band imaging data the FP photometric parameters (effective diameter and effective surface brightness) have been measured for 324 galaxies. The new spectroscopic and photometric data have been carefully combined with an extensive body of measurements compiled from the literature, to yield a closely homogeneous catalogue of FP data for 725 early type galaxies. Fitting the inverse FP relation to the merged catalogue yields distance estimates with a scatter of 22% per galaxy, resulting in cluster distance errors of 2-13%. The distances are consistent, on a cluster-by-cluster basis, with those determined from Tully-Fisher-Fisher studies and from earlier FP determinations. The distances are marginally inconsistent with distance estimates based on brightest cluster galaxies, but this disagreement can be traced to a few highly discrepant clusters. The resulting peculiar velocity field is dominated by a bulk streaming component, with amplitude of 810 ± 180km s(^-1) (directed towards l = 260 ,b = -5 ), a result which is robust against a range of potential systematic effects. The flow direction is ~35 from the CMB dipole and ~15 from the X-ray cluster dipole direction. Two prominent superclusters (the Shapley Concentration and the Horologium-Reticulum Supercluster) may contribute significantly to the generation of this flow. More locally, there is no far- side infall into the 'Great Attractor' (GA), apparently due to the opposing pull of the Shapley Concentration. A simple model of the flow in this direction suggests that the GA region generates no more than ~60% of the Local Group's motion in this direction. Contrary to some previous studies, the Perseus-Pisces supercluster is found to exhibit no net streaming motion. On small scales the velocity field is extremely quiet, with an rms cluster peculiar velocity of < 270 km s(^-1) in the frame defined by the bulk-flow. The results of this survey suggest that very distant mass concentrations contribute significantly to the local peculiar velocity field. This result is difficult to accommodate within currently popular cosmological models, which have too little large-scale power to generate the observed flow. The results may instead favour models with excess fluctuation power on 60-150h(^-1)Mpc scales.

The post-Newtonian (PN) perturbative framework has been successful in understanding the slow-motion, weak fi eld limit of Einstein's theory of gravity on solar system scales, and for isolated astrophysical systems. The parameterized post-Newtonian (PPN) formalism extended the PN framework to put very tight constraints on deviations from Einstein's theory on the aforementioned scales and systems. In this work, we extended and applied the post-Newtonian formalism to cosmological scales. We fi rst used it to construct a cosmological model to understand the effect of regularly arranged point sources on the background expansion. Here we found that at higher orders we obtained a small radiation-like correction to the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) equations, for a matter-dominated universe. This radiation-like correction was purely due to the inhomogeneity of our model, and the non-linearity of Einstein's eld equations. We also extended the post-Newtonian formalism to include other forms of matter that are cosmologically relevant, such as radiation and a cosmological constant, and studied the non-linear effects they might have on the background expansion. Then we constructed an extension of the parameterized post-Newtonian formalism (PPN) to cosmological scales. We used it to parameterize the background expansion of the universe as well as rst-order perturbations in cosmology, using four functions of time. In the future, this could allow us to put constraints on deviations from Einstein's theory of gravity on cosmological scales. We gave examples of how our parameterization would work for dark energy models and scalar-tensor and vector-tensor theories of gravity. In the nal part of this work, we studied how light propagation behaves in an inhomogeneous post-Newtonian cosmology with matter and a cosmological constant. We used it to understand the effect that inhomogeneities would have on observables such as angular diameter distances as compared to those that are expected from a homogeneous and isotropic FLRW universe.

Dark matter dominates the mass distribution of the universe, and dark energy determines its expansion. The two are the most mysterious and attractive subjects in modern cosmology, because they provide an opportunity to discover new fundamental physics. Cosmological weak gravitational lensing, which describes the deflection of photons by the gravitational force from large-scale structure in the universe, has been an active area of research in the past decade with many completed, ongoing, and upcoming surveys. Because weak lensing is sensitive to the growth of structure and expansion history of the universe, it is a great tool for improving our understanding of both dark matter and dark energy problems. Cosmic structures have become non-linear by gravitational clustering. The non-linear structures are important to weak lensing, and cause non-Gaussianity in the lensing maps. In this thesis, I study the influence of non-linearity and non-Gaussianity on the uncertainty of lensing measurements. I develop a new method to robustly measure the covariance matrix of the lensing convergence power spectrum, from simulations. Because 21-cm intensity map may soon cover half sky at redshift 1-4, I build optimal estimators for reconstructing lensing from the 21-cm sources. I develop Gaussian optimal estimators which can be derived nalytically, and non-Gaussian optimal estimators which can be constructed numerically from simulation data. I then run a large number of N-body simulations. For both lenses and 21-cm sources, I explore the statistical uncertainties in the simulation data. We show that the non-Gaussianity nature of lensing decreases the dark energy figure of merit by a factor of 1.3 to 1.6 for a few future surveys. We also find that the non-Gaussianity nature of the 21-cm sources reduces the signal to noise ratio by several orders of magnitude. The reconstruction noise saturates at mildly non-linear scales, where the linear power spectrum of the source is $\Delta^2\sim 0.2-0.5$. For 21-cm sources at $z\sim 2-4$, the lensing reconstruction is limited by cosmic variance at $\ell \lesssim 100$, which is in the linear regime of gravitational growth, and robustly predicted by theory. This allows promising constraints to various modified gravity and dark energy models.

Dark matter dominates the mass distribution of the universe, and dark energy determines its expansion. The two are the most mysterious and attractive subjects in modern cosmology, because they provide an opportunity to discover new fundamental physics. Cosmological weak gravitational lensing, which describes the deflection of photons by the gravitational force from large-scale structure in the universe, has been an active area of research in the past decade with many completed, ongoing, and upcoming surveys. Because weak lensing is sensitive to the growth of structure and expansion history of the universe, it is a great tool for improving our understanding of both dark matter and dark energy problems. Cosmic structures have become non-linear by gravitational clustering. The non-linear structures are important to weak lensing, and cause non-Gaussianity in the lensing maps. In this thesis, I study the influence of non-linearity and non-Gaussianity on the uncertainty of lensing measurements. I develop a new method to robustly measure the covariance matrix of the lensing convergence power spectrum, from simulations. Because 21-cm intensity map may soon cover half sky at redshift 1-4, I build optimal estimators for reconstructing lensing from the 21-cm sources. I develop Gaussian optimal estimators which can be derived nalytically, and non-Gaussian optimal estimators which can be constructed numerically from simulation data. I then run a large number of N-body simulations. For both lenses and 21-cm sources, I explore the statistical uncertainties in the simulation data. We show that the non-Gaussianity nature of lensing decreases the dark energy figure of merit by a factor of 1.3 to 1.6 for a few future surveys. We also find that the non-Gaussianity nature of the 21-cm sources reduces the signal to noise ratio by several orders of magnitude. The reconstruction noise saturates at mildly non-linear scales, where the linear power spectrum of the source is $\Delta^2\sim 0.2-0.5$. For 21-cm sources at $z\sim 2-4$, the lensing reconstruction is limited by cosmic variance at $\ell \lesssim 100$, which is in the linear regime of gravitational growth, and robustly predicted by theory. This allows promising constraints to various modified gravity and dark energy models.

The cosmology in the Hubble expansion era of the Horava-Witten M-theory compactified on a Calabi-Yau threefold is studied in the reduction to five-dimensions where the effects of the Calabi-Yau manifold are summarized by the volume modulus, and all perturbative potentials are included. Matter on the branes are treated as first order perturbations of the static vacuum solution, and all equations in the bulk and all boundary conditions on both end branes are imposed. It is found that for a static volume modulus and a static fifth dimension, y, one can recover the four dimensional Robertson-Friedmann-Walker cosmology for relativistic matter on the branes, but not for non-relativistic matter. For relativistic matter, the Hubble parameter H becomes independent of y to first order in matter density, and if a consistent solution for nonrelativistic matter exists it would require H to be y dependent. These results hold also when an arbitrary number of 5-branes are included in the bulk. The five dimensional Horava-Witten model is compared with the Randall Sundrum phenomenology with a scalar field in the bulk where a bulk and brane potential are used so that the vacuum solutions can be rigorously obtained.(In the Appendix, the difficulty of obtaining approximate vacuum solutions for other potentials is discussed.) In this case nonrelativistic matter is accommodated by allowing the distance between the branes to vary. It is suggested that non-perturbative potentials for the vacuum solution of Horava-Witten theory are needed to remove the inconsistency that non-relativistic matter creates. Also considered is the problem of gravitational forces between point particles on the branes in a Randall-Sundrum (R-S) two brane model with S1/Z2 symmetry. Matter is assumed to produce a perturbation to the R-S vacuum metric and all the 5D Einstein equations are solved to linearized order (for arbitrary matter on both branes). We show that while the gauge condition hi5 = 0, i = 0, 1, 2, 3 can always be achieved without brane bending, the condition h55 = 0 leads to large brane bending. The static potential arising from the zero modes and the corrections due to the Kaluza-Klein (KK) modes are calculated. Gravitational forces on the Planck (y1 = 0) brane recover Newtonian physics with small KK corrections (in accord with other work). However, forces on the TeV (y2) brane due to particles on that brane are strongly distorted by large R-S exponentials, making the model in disagreement with experiment if the TeV brane is the physical brane.

published_or_final_version / Physics / Master / Master of Philosophy

No description available.

No description available.

No description available.

No description available.