## Figures from this paper

figure 1 figure 2 figure 4 figure 6 figure 7 figure 8 figure 10 figure 11 figure 12 figure 14 figure 15 figure 17 figure 18 figure 19 figure 20 figure 21 figure 23 figure 24 figure 25 figure 26 figure 27 figure 28 figure 29 figure 30 figure 31 figure 32 figure 33 figure 34 figure 35 figure 36 figure 37 figure 38 figure 39 figure 40 figure 41 figure 42 figure 43 figure 44 figure 45 figure 46 figure 47

## 153 Citations

The Status of Cosmic Topology after Planck Data

- Physics
- 2016

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

- Physics, Art
- 2014

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

- Physics
- 2004

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…

Geometry and groups for cosmic topology

- Mathematics
- 2011

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

- PhysicsScience
- 2002

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

- Physics
- 2004

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

- Physics
- 2010

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

- Physics
- 2004

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

- Physics
- 2011

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…

## References

SHOWING 1-10 OF 331 REFERENCES

TEMPERATURE CORRELATIONS IN A FINITE UNIVERSE

- Physics
- 1999

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.

- PhysicsPhysical review letters
- 1993

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

- Physics
- 1999

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

- Physics
- 2000

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

- Physics
- 2001

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

- Physics
- 2000

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

- Physics
- 2000

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

- Mathematics
- 1998

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.

- MathematicsPhysical review letters
- 2001

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…