Topology and the cosmic microwave background

  title={Topology and the cosmic microwave background},
  author={Janna Levin},
  journal={Physics Reports},
  • J. Levin
  • Published 16 August 2001
  • Physics, Mathematics
  • Physics Reports
The Status of Cosmic Topology after Planck Data
In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background
Cosmic topology: Twenty years after
What is the shape of the Universe? Is it finite or infinite? Is space multi-connected to create ghost images of faraway cosmic sources? After a “dark age” period, the field of cosmic topology has now
Hyperbolic universes with a horned topology and the cosmic microwave background anisotropy
We analyse the anisotropy of the cosmic microwave background (CMB) in hyperbolic universes possessing a non-trivial topology with a fundamental cell having an infinitely long horn. The aim of this
Aps instability and the topology of the brane-world
Geometry and groups for cosmic topology
The Cosmic Microwave Background is measured by satellite observation with great precision. It offers insight into its origin in early states of the universe. Unexpected low multipole amplitudes of
Measuring Spacetime: From the Big Bang to Black Holes
Space is not a boring static stage on which events unfold over time, but a dynamic entity with curvature, fluctuations, and a rich life of its own. Spectacular measurements of the cosmic microwave
Statistical isotropy of the cosmic microwave background
The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra-large scale structure of the cosmos, in particular, of non-trivial cosmic topology. The
Cosmic microwave anisotropies in an inhomogeneous compact flat universe
The anisotropies of the cosmic microwave background (CMB) are computed for the half-turn space E_2 which represents a compact flat model of the Universe, i.e. one with finite volume. This model is
Creation of a compact topologically nontrivial inflationary universe
If inflation can occur only at the energy density V much smaller than the Planck density, which is the case for many inflationary models based on string theory, then the probability of quantum
Vacuum Energy and the Topology of the Universe
We analyze the dependence of the quantum vacuum energy on the space topology. In particular we point out the existence of a renormalization ambiguity in spaces with non-vanishing curvature. The


We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all
Microwave background anisotropy in a toroidal universe.
Large-scale cosmic microwave background temperature fluctuations are calculated for a universe with the topology of a 3-torus and it is found that a topologically ``small'' universe is no longer an interesting cosmological model.
The Fluctuations of the Cosmic Microwave Background for a Compact Hyperbolic Universe
The fluctuations of the cosmic microwave background (CMB) are investigated for a small, open universe, i.e., one that is periodically composed of a small fundamental cell. The evolution of initial
A small universe after all
The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply
The cosmic microwave background for a nearly flat compact hyperbolic universe
The fluctuations of the cosmic microwave background (CMB) are investigated for a hyperbolic universe with finite volume. Four-component models with radiation, matter, vacuum energy and an extra
Temperature correlations in a compact hyperbolic universe
The effect of a non-trivial topology on the temperature correlations of the cosmic microwave background (CMB) in a small compact hyperbolic universe with volume comparable to the cube of the
The Angular Scale of Topologically-Induced Flat Spots in the Cosmic Microwave Background Radiation
The notion that the topology of the universe need not be that of the universal covering space of its geometry has recently received renewed attention. Generic signatures of cosmological topology have
A New approach to string cosmology
We discuss quotients of Anti-de Sitter (AdS) spacetime by a discrete group in light of the AdS-CFT correspondence. Some quotients describe closed universes which expand from zero volume to a maximum
Homogeneity, flatness, and "large" extra dimensions.
We consider a model in which the Universe is the direct product of an ordinary (3+1)-dimensional space--a brane where all the standard model fields are confined-and a compact hyperbolic manifold. The