A Cosmic Microwave Background feature consistent with a cosmic texture

The Cosmic Microwave Background provides our most ancient image of the Universe and our best tool for studying its early evolution. Theories of high energy physics predict the formation of various types of topological defects in the very early universe, including cosmic texture which would generate hot and cold spots in the Cosmic Microwave Background. We show through a Bayesian statistical analysis that the most prominent, 5 degree radius cold spot observed in all-sky images, which is otherwise hard to explain, is compatible with having being caused by a texture. From this model, we constrain the fundamental symmetry breaking energy scale to be phi_0 ~ 8.7 x 10^(15) GeV. If confirmed, this detection of a cosmic defect will probe physics at energies exceeding any conceivable terrestrial experiment.Comment: Accepted by Science. Published electronically via Science Express on 25 October 2007, http://www.sciencemag.org/cgi/content/abstract/114869

The prospects for African urban economies

Cities generally function as sources of economic development and human progress. One of the puzzles about Africa's urbanization is that it has not been accompanied by greater economic dynamism. The paper considers the distinctive development trajectory of African urban economies. It considers the applicability of the argument that cities are drivers of economic growth, and the idea that cities develop more complex, higher-value functions over time. It examines the recent revival of African economies, and asks whether the fashionable idea of enhanced international integration through cross-border collaboration might facilitate greater urban prosperity

Inflation after Planck and BICEP2

We discuss the inflationary paradigm, how it can be tested, and how various models of inflation fare in the light of data from Planck and BICEP2. We introduce inflation and reheating, and discuss temperature and polarisation anisotropies in the cosmic microwave background radiation due to quantum fluctuations during inflation. Fitting observations of the anisotropies with theoretical realisations obtained by varying various parameters of the curvature power spectrum and cosmological parameters enables one to obtain the allowed ranges of these parameters. We discuss how to relate these parameters to inflation models which allows one to rule in or out specific models of inflation.Comment: Slightly longer version of a plenary review talk at the XXI DAE-BRNS High Energy Physics Symposium at IIT Guwahati, Dec.8-12, 2014. 14 pages, 7 fig

Stability of Flat Space to Singular Instantons

Hawking and the author have proposed a class of singular, finite action instantons for defining the initial conditions for inflation. Vilenkin has argued they are unacceptable. He exhibited an analogous class of asymptotically flat instantons which on the face of it lead to an instability of Minkowski space. However, all these instantons must be defined by introducing a constraint into the path integral, which is then integrated over. I show that with a careful definition these instantons do not possess a negative mode. Infinite flat space is therefore stable against decay via singular instantons.Comment: 9 pages, RevTex file, including two postscript figure files. Minor typos corrected, figure improve

Singular Instantons Made Regular

The singularity present in cosmological instantons of the Hawking-Turok type is resolved by a conformal transformation, where the conformal factor has a linear zero of codimension one. We show that if the underlying regular manifold is taken to have the topology of $RP^4$, and the conformal factor is taken to be a twisted field so that the zero is enforced, then one obtains a one-parameter family of solutions of the classical field equations, where the minimal action solution has the conformal zero located on a minimal volume noncontractible $RP^3$ submanifold. For instantons with two singularities, the corresponding topology is that of a cylinder $S^3\times [0,1]$ with D=4 analogues of `cross-caps' at each of the endpoints.Comment: 23 pages, compressed and RevTex file, including nine postscript figure files. Submitted versio

Deconstructing density: strategic dilemmas confronting the post-Apartheid city

Public authorities in many countries around the world are seeking to raise urban densities. Residential densification is particularly important in South Africa because of the colonial and apartheid legacy of sprawling, fragmented, racially divided cities. The paper examines the case for densifying central Cape Town and provides a framework to help deconstruct the concept and explore the policy challenges faced. It focuses on the bold aim to treble the area’s population within 10 years, and identifies issues where further consideration and public debate are required for how this can be achieved in a way that is desirable, affordable and fair. A key message is the need to understand both the composition of demand for central city living and the challenges involved in supplying suitable housing and amenities at higher densities. The level of social inequality in the city poses greater complications than elsewhere