Why Not Consider Closed Universes?

We consider structure formation and CMB anisotropies in a closed universe, both with and without a cosmological constant. The CMB angular power spectrum and the matter transfer function are presented, along with a discussion of their relative normalization. This represents the first full numerical evolution of density perturbations and anisotropies in a spherical geometry. We extend the likelihood function vs. Omega from the COBE 2-year data to Omega>=1. For large Omega the presence of a very steep rise in the spectrum towards low ell allows us to put an upper limit of Omega<=1.5 (95%CL) for primordial spectra with n<=1. This compares favorably with existing limits on Omega. We show that there are a range of closed models which are consistent with observational constraints while being even older than the currently popular flat models with a cosmological constant. Future constraints from degree scale CMB data may soon probe this region of parameter space. A derivation of the perturbed Einstein, fluid and Boltzmann equations for open and closed geometries is presented in an appendix.Comment: 24 pages, including 13 figures in a uuencoded self-unpacking shell script. Submitted to Ap

Perturbative analysis on infrared aspects of noncommutative QED on R^4

Here we examine the noncommutative counterpart of QED, which is called as noncommutative QED. The theory is obtained by examining the consistent minimal coupling to noncommutative U(1) gauge field. The *-product admits the coupling of the matter with only three varieties of charges, i.e., 0, +1 and -1. Ultraviolet divergence can be absorbed into the rescaling of the fields and the parameters at least at one loop level. To examine the infrared aspect of the theory the anomalous magnetic dipole moment is calculated. The dependence on the direction of photon momentum reflects the Lorentz symmetry violation of the system. The explicit calculation of the finite part of the photon vacuum polarization shows the singularity ln({q C^TC q}) (C^{\mu\nu} is a noncommutative parameter.) in the infrared side which also exists in noncommutative Yang-Mills theory. It is associated with the ultraviolet behavior of the theory. We also consider the extension to chiral gauge theory in the present context, but the requirement of anomaly cancellation allows only noncommutative QED.Comment: 10 pages, LaTEX2e, A part of results changed, reference adde

A Characteristic Scale on the Cosmic Microwave Sky

The current suite of results from Cosmic Microwave Background anisotropy experiments is fulfilling the promise of providing extraordinary levels of discrimination between cosmological models. We calculate a binned anisotropy power spectrum, which we tabulate, along with error bars and bin-to-bin correlations, so that it can be easily used for constraining models. The resulting power spectrum is flat at large angles, with a gradual rise to a prominent peak at around 0.5 degrees and a decrease thereafter. This is precisely the shape predicted by inflationary-inspired adiabatic models. Within that class of cosmologies, this characteristic scale imprinted on the CMB sky can be used to infer that the geometry of the Universe is very close to flat. The next wave of CMB results should add fuel to the debate about whether or not the Universe once inflated, as well as beginning in earnest the task of measuring cosmological parameters.Comment: 6 pages, 1 figure. A less technical article based on the same work has appeared in Science Perspectives under the title "How Flat is the Universe?" (Science, Mar 24, 2000, 2171-2172

Topology and Dark Energy: Testing Gravity in Voids

Modified gravity has garnered interest as a backstop against dark matter and dark energy (DE). As one possible modification, the graviton can become massive, which introduces a new scalar field - here with a Galileon-type symmetry. The field can lead to a nontrivial equation of state (EOS) of DE which is density-and-scale-dependent. Tension between Type Ia supernovae and Planck could be reduced. In voids the scalar field dramatically alters the EOS of DE, induces a soon-observable gravitational slip between the two metric potentials, and develops a topological defect (domain wall) due to a nontrivial vacuum structure for the field.Comment: Revised version, added detail, conclusions unchanged, matches PRL published version in content. 4 pages, 2 figure

"Sample Variance" in Small-Scale CMB Anisotropy Experiments

We discuss the effects of finite sky coverage and the uncertainty in extracting information about the power spectrum from experiments on small angular scales. In general the cosmic variance is enhanced by a factor of $4\pi/A$, where $A$ is the solid angle sampled by the experiment. As a rough guide, an experiment with sensitivity peaking at the $\ell$th multipole has to cover \simgt\ell independent patches to have a lower ``sample variance'' than for a whole-sky measurement of the quadrupole. Our approach gives a relatively simple way of attaching an error bar to the theoretical prediction for a particular experiment, and thereby comparing theories with experimental results, without the need for computationally-intensive Maximum Likelihood or Monte Carlo calculations.Comment: 6 pages in Plain TeX with 1 postscript figure appende