Bianchi type I cyclic cosmology from Lie-algebraically deformed phase
  space
  We study the effects of noncommutativity, in the form of a Lie-algebraically
deformed Poisson commutation relations, on the evolution of a Bianchi type I
cosmological model with a positive cosmological constant. The phase space
variables turn out to correspond to the scale factors of this model in $x$, $y$
and $z$ directions. According to the conditions that the structure constants
(deformation parameters) should satisfy, we argue that there are two types of
noncommutative phase space with Lie-algebraic structure. The exact classical
solutions in commutative and type I noncommutative cases are presented. In the
framework of this type of deformed phase space, we investigate the possibility
of building a Bianchi I model with cyclic scale factors in which the size of
the universe in each direction experiences an endless sequence of contractions
and re-expansions. We also obtain some approximate solutions for the type II
noncommutative structure by numerical methods and show that the cyclic behavior
is repeated as well. These results are compared with the standard commutative
case, and similarities and differences of these solutions are discussed.
