We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a de tection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters. 10Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip. Striking advances in observational cosmology over the past two decades have provided us with a consistent account of the form and composition of the universe. Now that key cosmological parameters have been determined to within a few percent, we anticipate a generation of experiments that move beyond adding precision to measurements of what the universe is made of, but instead help us learn why the universe has the form we observe. In particular, during the coming decade, observational cosmology will probe the detailed dynamics of the universe in the earliest instants after the Big Bang, and start to yield clues about the physical laws that governed that epoch. Future experiments will plausibly reveal the dynamics responsible both for the large-scale homogeneity and flatness of the universe, and for the primordial seeds of small-scale inhomogeneities, including our own galaxy.The leading theoretical paradigm for the initial moments of the Big Bang is inflation [1][2][3][4][5][6], a period of rapid accelerated expansion. Inflation sets the initial conditions for conventional Big Bang cosmology by driving the universe towards a homogeneous and spatially flat configuration, which accurately describes the average state of the universe. At the same time, quantum fluctuations in both matter fields and spacetime produce minute inhomogeneities [7][8][9][10][11][12]. The seeds that grow into the galaxies, clusters of galaxies and the temperature anisotropies in the cosmic microwave background (CMB) are thus planted during the first moments of the universe's existence. By measuring the anisotropies in the microwave background and the large scale distribution of galaxies in the sky, we can infer the spectrum of the primordial perturbations laid down during inflation, and thus probe the underlying physics of this era. Any successful inflationary model will deliver a universe that is, on average, spatially flat and homogeneous -and one homogeneous universe looks very much like ano...
Using a large N sigma model approximation we explicitly calculate the power spectrum of gravitational waves arising from a global phase transition in the early universe and we confirm that it is scale invariant, implying an observation of such a spectrum may not be a unique feature of inflation. Moreover, the predicted amplitude can be over 3 orders of magnitude larger than the naive dimensional estimate, implying that even a transition that occurs after inflation may dominate in Cosmic Microwave Background polarization or other gravity wave signals.In 1992 [1] it was proposed on dimensional grounds that a scalar field which undergoes a symmetry breaking phase transition can give rise to a scale-invariant spectrum of gravitational waves by virtue of causality: the correlation length of the field is of order the horizon size, as the horizon grows, uncorrelated regions come into contact, and the field releases energy as it relaxes.Following the detection of both temperature and polarization fluctuations in the Cosmic Microwave Background (CMB), there is now great interest in the possibility of using CMB measurements to probe for a nearly scale invariant gravitational wave spectrum that is widely considered to be the "smoking gun" of inflation [2]. Long wavelength primordial gravitational radiation would affect the polarization of the CMB [3].Given the importance therefore of a possible observation of a gravitational wave signature in the CMB, and proposed missions capable of observing CMB polarization such as CMBPol and Planck it is imperative to go beyond dimensional arguments and explore the detailed nature of the spectrum of radiation produced by another mechanism such as that in [1] from which the inflationary spectrum would need to be discriminated. This is the purpose of the present work.Our analysis proceeds in two stages. First we analyze the ordering of a symmetry breaking scalar field evolving in a flat FRW background. Then we compute the gravitational radiation produced by the relaxation of the scalar field. The estimates given in [1] assumed a two component scalar field in a Mexican hat potential. However the two component case presents special complications due to the possibility that strings will form and frustrate the ordering. For this reason we work with an N -component field and work in the sigma model limit. In other words we impose the constrainton N otherwise free massless fields. Here η is the vacuum expectation value of the field. Due to the constraint the equations of motion for this system are non-linear and in general can only be solved numerically. However it has long been known in the condensed matter literature on ordering kinetics that the problem becomes tractable in the large N limit; that large N method was adapted to the study of global phase transitions in cosmology by Turok and Spergel [4] whose analysis we will follow.A key approximation in the large N solution is to replace the trace of the stress-tensor with its spatial average in the sigma model equation of motion. Thus we s...
We investigate the contentions that Jackson Pollock's drip paintings are fractals produced by the artist's Lévy distributed motion and that fractal analysis may be used to authenticate works of uncertain provenance. We find that the paintings exhibit fractal characteristics over too small a range to be usefully considered as fractal; their limited fractal characteristics are easily generated without Lévy motion, both by freehand drawing and gaussian random motion. Several problems must therefore be addressed before fractal analysis can be used to authenticate paintings.
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