  The kinematical phase space of classical gravitational field is flat (affine)
and unbounded. Because of this, field variables may tend to infinity leading to
appearance of singularities, which plague Einstein's theory of gravity. The
purpose of this article is to study the idea of generalizing the theory of
gravity by compactification of the phase space. We investigate the procedure of
compactification of the phase space on a minisuperspace gravitational model
with two dimensional phase space. In the affine limit, the model reduces to the
flat de Sitter cosmology. The phase space is generalized to the spherical case,
and the case of loop quantum cosmology is recovered in the cylindrical phase
space limit. Analysis of the dynamics reveals that the compactness of the phase
space leads to both UV and IR effects. In particular, the phase of re-collapse
appears, preventing the universe from expanding to infinite volume.
Furthermore, the quantum version of the model is investigated and the quantum
constraint is solved. As an example, we analyze the case with the spin quantum
number $s=2$, for which we determine transition amplitude between initial and
final state of the classical trajectory. The probability of the transition is
peaked at $\Lambda=0$.
