--- title: "Detectability of cosmic topology in flat universes • CBPF Index" description: "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." canonical_url: "https://index.cbpf.br/es/publicacoes/6ad2a767639f62b11adbb03e" locale: es meta: "og:description": "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Detectability%2Bof%2Bcosmic%2Btopology%2Bin%2Bflat%2Buniverses%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_~Ry5JLiBHb21lcm87IE1hcmNlbG8gSm9zw6kgUmVib3XDp2Fz%2Cdetalhe_2002%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIwM2Ui%2Cs_kiZd3MmaPZ-v4ssj.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Detectability of cosmic topology in flat universes • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Detectability%2Bof%2Bcosmic%2Btopology%2Bin%2Bflat%2Buniverses%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_~Ry5JLiBHb21lcm87IE1hcmNlbG8gSm9zw6kgUmVib3XDp2Fz%2Cdetalhe_2002%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIwM2Ui%2Cs_kiZd3MmaPZ-v4ssj.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Nota de Física****Publicado** # **Detectability of cosmic topology in flat universes** **G.I. Gomero; Marcelo José Rebouças** 2002 [**Descargar PDF **0,2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb03e/pdf) [**Contactar al responsable**](mailto:apub@cbpf.br?subject=Detectability%20of%20cosmic%20topology%20in%20flat%20universes) ## **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
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