Generalized uncertainty principle in quantum cosmology for the maximally
  symmetric space
  The new uncertainty relation is derived in the context of the canonical
quantum theory with gravity for the case of the maximally symmetric space. This
relation establishes a connection between fluctuations of the quantities which
determine the intrinsic and extrinsic curvatures of the spacelike hypersurface
in spacetime and introduces the uncertainty principle for quantum gravitational
systems. The generalized time-energy uncertainty relation, which takes into
account gravity, is proposed. It is shown that known Unruh's uncertainty
relation follows, as a particular case, from the new uncertainty relation. As
an example, the sizes of fluctuations of the scale factor and its conjugate
momentum are calculated within an exactly solvable model. All known
modifications of the uncertainty principle deduced previously from different
approaches in the theory of gravity and string theory are obtained as
particular cases of the proposed general expression.
