The spectrum of density perturbations is calculated in the new-inflationary-universe scenario. The main source is the quantum fluctuations of the Higgs field, which lead to fluctuations in the time at which the false vacuum energy is released. The value of bp/p on any given length scale l, at the time when the Hubble radius » l, is estimated. This quantity is nearly scale invariant (as desired), but is unfortunately about 10' times too large. PACS numbers: 98.80. Bp, 12.10.En, 98.50.Eb, 98.80.DrThe inflationary-universe scenario was proposed by one of us' as a possible solution to the horizon, flatness, and monopole problems. In this scenario the universe supercools by many orders of magnitude below the critical temperature of a grand unified theory (GUT) phase transition, and in the process it exponentially expands by an enormous factor. The original version required that eventually the bubbles of the new phase would coalesce to fill the space uniformly. It was pointed out in the original paper, however, that under plausible assumptions this requirement is not fulfilled. Further studies" have shown that there is no apparent way to achieve a smooth coalescence of bubbles in the aftermath of inflation.The hopes for the inflationary universe brightened considerably when Linde and Albrecht and Steinhardt' proposed an alternative ending which avoids the problems described above. In this new inflationary universe, " the entire observed universe emerges from a single bubble or fluctuation. While a generic potential would lead to bubbles with far too little entropy to comprise the observed universe, ' these authors showed that with a Coleman-Weinberg potential' it is very plausible that a single bubble or fluctuation can undergo enough inflation to avoid this problem. The universe expands exponentially as the Higgs field p slowly ' rolls" down the potential, and the energy is then rapidly thermalized when p begins to oscillate about its minimum.In this paper we will examine the consequences of the quantum fluctuations of the scalar field p which occur during the era of exponential expansion. We will follow the evolution of these fluctuations through the time at which galactic scales come within the Hubble radius (at about 10' sec), and we will estimate the energy density fluctuations Dpi'p at that time. According to Harrison and Zeldovich' this number should be about 10 ', and roughly independent of scale. We find that the new inflationary universe leads to a 5p/p which is roughly independent of scale, but with a magnitude of = 50. Thus, it appears that a further modification of this scenario is necessary in order to make it workable.For concreteness we will deal with an SU (5)

General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v µ -an external quantity, which we fix to be a non-vanishing constant in its time component. The theory is identical to one in which the embedding coordinate is itself a dynamical variable, rather than a fixed, external quantity. Consequently diffeomorphism symmetry breaking is hidden in the modified theory: the Schwarzschild metric is a solution; gravitational waves possess two polarizations, each traveling at the velocity of light; a conserved energy-momentum (pseudo-) tensor can be constructed. The modification is visible in the intensity of gravitational radiation: the two polarizations of a gravity wave carry intensities that are suppressed/enchanced by the extension. *

Jackiw and Pi Reply: That our soliton profiles satisfy the requisite equations is of course verified without encountering distributions: The original field equations are nonsingular, the profiles are nonsingular, and straightforward differentiation establishes that the profiles indeed solve the equations. To derive our solutions one may use singular coordinates, as we do in Ref. 1. Or one may ignore singular points in the coordinate system by invoking continuity of the nonsingular solutions; this is the strategy of Ref, 2. Hagen 3 adopts a method, which has already appeared in the literature, 4 wherein singular coordinates are avoided. Still other approaches are available. 5 It matters not whether one uses singular or nonsingular coordinates, provided singularities are treated consistently and are absent from the final solutions. That we achieve this desired goal is self-evident.In one approach to the consistent handling of singularities, we use an unfamiliar and unconventional representation for the planar 8 function, !

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We construct a chiral gauge theory to describe fractionalization of fermions in graphene. Thereby we extend a recently proposed model, which relies on vortex formation. Our chiral gauge fields provide dynamics for the vortices and also couple to the fermions.