The Sachs-Wolfe effect

Bibliography: pages 112-113.This thesis discusses the Sachs-Wolfe effect, which is the variation in the observed temperature of radiation emitted at the last scattering surface which occurs at the place where matter and radiation decouple at about 4000 degrees Kelvin. The work is in two parts, with the first part dealing with extensions made by George Ellis, Chongming Xu, Bill Stoeger and myself to the paper by Miroslaw Panek [13] where the gauge invariant formalism of cosmological density perturbations by James Bardeen [1] has been used to find the SW effect in the case of a perturbed Friedman-Lemaitre-Robertson-Walker (FLRW) universe with a barotropic equation of state describing the matter in the unperturbed case. In our work we extend the example given by Panek for a flat universe (K = 0) filled with dust where the density perturbations are adiabatic, to the case of non-fl.at universes (K = -1, 0 + 1) filled with a mixture of N types of matter where the density perturbations are nonadiabatic. The second part shows the agreement between the formalisms of Sachs and Wolfe's pioneering paper and the recent work of George Ellis and Marco Bruni which presents the study of cosmological perturbations in a gauge invariant and covariant way. After the overview of the work covered in this thesis, the gauge invariant formulation of Bardeen is discussed where we follow the description by Panek of a universe whose energy content is described by a mixture of N ideal fluids coupled only by gravity. From the Einstein equations we get Bardeen's evolution equation for the gauge invariant energy density perturbation which is now given for the N different matter fluids as it appears in Panek. We then checked Panek's equations where he finds an expression for the placing of the perturbed last scattering surface, after which he derives an equation for the fractional temperature variation and writes it in terms of the perturbation variables. The equation found by SW for their particular choice of K = O, pressure free dust, where the last scattering surface is placed at its unperturbed position, is verified in terms of the Bardeen formalism. Now we extend this simple case to nonadiabatic perturbations in the same scenario and find the SW effect for a mixture of two fluids: dust and radiation, with nonadiabatic perturbations in a not necessarily flat universe. We then generalise to the case of a mixture or baryons and radiation and N types of matter. This section then ends with a calculation of the difference between temperatures taken from two different directions in the sky and is written in terms of the fractional temperature perturbation defined by Panek. The second part puts forward the formulation of the gauge problem by Ellis and Bruni (EB), and then writes out their gauge invariant quantities in terms of the SW variables. Their evolution equations are verified in this form, and the shear and vorticity determined as well. Now all of the EB cosmological quantities are listed for the special gauge that SW use and then we explore the relation between the SW metric and that of Bardeen before ending off by verifying that the form for the redshift in the EB approach is in agreement with that given by Panek

Better than before : comparing Moscow’s Cold War and Putin era policies toward Arabia and the Gulf

In comparing Soviet era and Putin era foreign policies toward Arabia and the Gulf, a striking similarity emerges. In both eras, Moscow’s foreign policy has been characterized not so much by a grand design but by an opportunistic approach that seeks to have good relations simultaneously with both anti-Western and pro-Western actors, including those bitterly opposed to each other. At the heart of Moscow’s approach both then and now has been an effort by Moscow to balance between opposing parties and thereby derive benefits from both. Moscow’s logic in both eras seems to have been based on the expectation that governments and other actors will calculate that they are better off having good relations with Moscow despite its support for their adversaries since Moscow might well support those adversaries even more otherwise. This paper will show how Moscow has often pursued this “balancing between adversaries” approach in Arabia and the Gulf both in the Cold War when the Soviet Union was pursuing a revolutionary foreign policy and in the Putin era when Russia has been pursuing a status quo-oriented foreign policy. This will shed light on the enduring nature both of the foreign policy goals that Moscow pursues in this region and of the means by which it does so. I will argue, though, that Putin has been more successful at this approach than the Soviets were, but that it still involves important limitations and risks for Moscow. Moscow, of course, has not just pursued this balancing between adversaries strategy in Arabia and the Gulf, but has done so in other regions—or would certainly like to. Nor is Russia the only great power to have adopted this approach. The question being addressed here, though, is how successful Moscow has been in pursuing this approach in this one key region. I will first describe the similar balancing efforts that Moscow pursued (sometimes successfully and sometimes not) during both the Cold War and the Putin eras toward the countries of this region: Saudi Arabia; the smaller Arab Gulf states; the Yemen(s); and Iraq and Iran. I will then examine the broader similarities in Moscow’s foreign policies toward the region during both eras, and discuss their strengths and weaknesses then and now

Assessing the political stability of Oman

"Compared to neighboring Saudi Arabia, there is very little press coverage on Oman. And unlike the many stories about how bad things are in the kingdom, the little reporting done on the sultanate is generally positive. It would be a mistake, however, to conclude from Oman’s glowing press coverage that all is well there. Oman, in fact, is experiencing some very difficult problems that are likely to get worse in coming years."(...