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...

We show that the effects of spin-orbit interaction in disordered conductors are manifestations of the Aharonov-Casher effect in the same sense as the effects of weak magnetic fields are manifestations of the Aharonov-Bohm effect. We propose that, in semiconducting samples, conductance oscillations should occur due to the Aharonov-Casher effect, whose observation would constitute a thousandfold improvement in its measurement. As in the disordered Aharonov-Bohm effect, these oscillations have half the period expected from the conventional Aharonov-Casher effect. PACS numbers: 71.70.Ej, 03.65.Bz, 72.15.Rn, 73.20.FzAharonov and Bohm showed long ago that a magnetic field enters quantum mechanics in two distinct ways, a distinction most easily described in the semiclassical limit. In this limit, first the magnetic field determines the classical trajectory of the particle through the Lorentz force law (the dynamical effect), and second it contributes to the phase accumulated along the trajectory through the line integral of the vector potential along it (the geometric effect). The latter effect has no classical analog. The term Aharonov-Bohm (AB) effect is now commonly used even in situations for which the dynamical effect is not rigorously zero, but is negligible compared to the geometric effect.In this sense there are now many well-known manifestations of the AB effect in the low-temperature transport properties of disordered normal conductors, e.g., weak- localization (WL) magnetoresistance [1], and the closely related Altshuler-Aronov-Spivak (AAS) effect [2], universal magnetoconductance fluctuations of mesoscopic samples [3], and persistent currents (AB magnetization) of arrays of rings [4]. In all of these phenomena weak magnetic fields (-100 G) are observed to have a significant effect at low T even though co c r<^\ (co c is the cyclotron frequency and r is the elastic scattering time), indicating that the dynamical role of the magnetic field is negligible compared to the impurity scattering. Low temperature is necessary so that the phase of the electron (which is smeared by inelastic scattering) remains well defined over large distances (typically /xm). As in the ideal AB effect, periodic oscillations with enclosed magnetic flux are observed in multiply connected geometries, however, with an important complication unique to the disordered AB effect. Measurements on single rings show the fundamental hc/e periodicity expected, whereas measurements on arrays of rings or cylinders show a shorter period he lie which is now understood to arise due to the effective disorder averaging which occurs when measuring many units at once [5]. Thus there is an effective charge doubling (e-+2e) which is a special feature of the disorder-averaged response to a vector potential. Recently Aharonov and Casher (AC) [6] have noted an analog (more precisely, an electromagnetic dual) of the AB effect in the influence of electric fields on neutral

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...

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