# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Bianchi type I universe with viscous fluid. (English) Zbl 1084.83512
Summary: We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant ${\Lambda }$. The role of viscous fluid and ${\Lambda }$ term in the evolution the BI spacetime is studied. Though the viscosity cannot remove the cosmological singularity, it plays a crucial part in the formation of a qualitatively new behavior of the solutions near singularity. It is shown that the introduction of the ${\Lambda }$ term can be handy in the elimination of the cosmological singularity. In particular, in case of a bulk viscosity, a negative ${\Lambda }$ provides a never-ending process of evolution, whereas, for some positive values of ${\Lambda }$ and the bulk viscosity being inverse proportional to the expansion, the BI Universe admits a singularity-free oscillatory mode of expansion. In case of a constant bulk viscosity and share viscosity being proportional to expansion, the model allows both non-periodic and inflationary expansion independent to the sign of ${\Lambda }$ term.
##### MSC:
 83C55 Macroscopic interaction of the gravitational field with matter (general relativity) 83F05 Relativistic cosmology