Cosmic String Signatures in the Cosmic Microwave Background Anisotropies

We briefly review certain aspects of cosmic microwave background anisotropies as generated in passive and active models of structure formation. We then focus on cosmic strings based models and discuss their status in the light of current high-resolution observations from the BOOMERanG, MAXIMA and DASI collaborations. Upcoming megapixel experiments will have the potential to look for non-Gaussian features in the CMB temperature maps with unprecedented accuracy. We therefore devote the last part of this review to treat the non-Gaussianity of the microwave background and present a method for computation of the bispectrum from simulated string realizations.Comment: Review article to appear in the special issue of New Astronomy Reviews dedicated to the memory of Dennis William Sciama, eds. Francesco Melchiorri, Yoel Rephaeli and Joseph Sil

Conformal invariance in 2-dimensional discrete field theory

A discretized massless wave equation in two dimensions, on an appropriately chosen square lattice, exactly reproduces the solutions of the corresponding continuous equations. We show that the reason for this exact solution property is the discrete analog of conformal invariance present in the model, and find more general field theories on a two-dimensional lattice that exactly solve their continuous limit equations. These theories describe in general non-linearly coupled bosonic and fermionic fields and are similar to the Wess-Zumino-Witten model.Comment: 18 pages, RevTeX, 2 figures included; revision of title and introductio

Minkowski Functional Description of Microwave Background Gaussianity

A Gaussian distribution of cosmic microwave background temperature fluctuations is a generic prediction of inflation. Upcoming high-resolution maps of the microwave background will allow detailed tests of Gaussianity down to small angular scales, providing a crucial test of inflation. We propose Minkowski functionals as a calculational tool for testing Gaussianity and characterizing deviations from it. We review the mathematical formalism of Minkowski functionals of random fields; for Gaussian fields the functionals can be calculated exactly. We then apply the results to pixelized maps, giving explicit expressions for calculating the functionals from maps as well as the Gaussian predictions, including corrections for map boundaries, pixel noise, and pixel size and shape. Variances of the functionals for Gaussian distributions are derived in terms of the map correlation function. Applications to microwave background maps are discussed.Comment: 24 pages with 2 figures. Submitted to New Astronom

Predictability crisis in inflationary cosmology and its resolution

Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated in the literature. Because of the infinite thermalized volume resulting from eternal inflation, it has proven difficult to obtain a meaningful and unambiguous probability distribution for observables, in particular due to the gauge dependence. In the present paper, we further develop the gauge-invariant procedure proposed in a previous work for models with a continuous variation of "constants". The recipe uses an unbiased selection of a connected piece of the thermalized volume as sample for the probability distribution. To implement the procedure numerically, we develop two methods applicable to a reasonably wide class of models: one based on the Fokker-Planck equation of stochastic inflation, and the other based on direct simulation of inflationary spacetime. We present and compare results obtained using these methods.Comment: 23 pages, 13 figure

Uncertainties of predictions in models of eternal inflation

In a previous paper \cite{MakingPredictions}, a method of comparing the volumes of thermalized regions in eternally inflating universe was introduced. In this paper, we investigate the dependence of the results obtained through that method on the choice of the time variable and factor ordering in the diffusion equation that describes the evolution of eternally inflating universes. It is shown, both analytically and numerically, that the variation of the results due to factor ordering ambiguity inherent in the model is of the same order as their variation due to the choice of the time variable. Therefore, the results are, within their accuracy, free of the spurious dependence on the time parametrization.Comment: 30 pages, RevTeX, figure included, added some references and Comments on recent proposal (gr-qc/9511058) of alternative regularization schemes, to appear in Phys. Rev.

Particle creation in a tunneling universe

An expanding closed universe filled with radiation can either recollapse or tunnel to the regime of unbounded expansion, if the cosmological constant is nonzero. We re-examine the question of particle creation during tunneling, with the purpose of resolving a long-standing controversy. Using a perturbative superspace model with a conformally coupled massless scalar field, which is known to give no particle production, we explicitly show that the breakdown of the semiclassical approximation and the ``catastrophic particle production'' claimed earlier in the literature are due to an inappropriate choice of the initial quantum state prior to the tunneling.Comment: 21 pages, 3 embedded figures, RevTeX