Nota de FísicaPublicado
Detectability of cosmic topology in flat universes
G.I. Gomero; Marcelo José Rebouças
2002
Datos de la publicación
- Autores
- G.I. Gomero; Marcelo José Rebouças
- Tipo
- Nota de Física
- Estado
- Publicado
- Fecha de publicación
- 2002
- Descripción
- A combination of recent astrophysical and cosmological observations seems to indicate that we live in an accelerating Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe whose spatial sections are nearly or exactly f\/lat ($\Omega_0 \simeq 1$). Motivated by this, and in order to complete our previous investigations on the detectability of \emph{nearly} f\/lat hyperbolic and spherical universes, we study here the problem of observational detection of the topology of FLRW universes with (exactly) f\/lat spatial sections. To this end, we f\/irst give a complete description of the dif\/feomorphic classif\/ication of compact f\/lat $3$-manifolds, and determine the expressions for the injectivity radii ($r_{inj}$), and for the volume of each class of Euclidean $3$-manifolds. There emerges from our calculations the undetectability conditions for each (topological) class of f\/lat universes. We also study how the bounds provided by recent cosmological observations can be used to identify f\/lat models having undetectable topologies. To materialize and quantify the study of the detectability of f\/lat topologies we use the undetectability conditions and an assumption by Bernshte\v{\i}n and Shvartsman which permits to establish a relation between topological typical lengths to the dynamics of f\/lat models. As a particular result we show that none of the models of two specif\/ic classes of f\/lat universes which satisfy the Bernshte\v{\i}n and Shvartsman condition has an undetectable topology, even if current catalogues of clusters of galaxies are used. A modif\/ied version of Bernshte\v{\i}n-Shvartsman assumption is also suggested and used to construct a great number of f\/lat universes with undetectable topology, even if cosmic microwave background radiation is used.
- Año
- 2002
- Número
- CBPF-NF-010/02
- Vínculo con tesis
- No
- Vínculo con beca
- No