Generic absence of strong singularities and geodesic completeness in
  modified loop quantum cosmologies
  Different regularizations of the Hamiltonian constraint in loop quantum
cosmology yield modified loop quantum cosmologies, namely mLQC-I and mLQC-II,
which lead to qualitatively different Planck scale physics. We perform a
comprehensive analysis of resolution of various singularities in these modified
loop cosmologies using effective spacetime description and compare with earlier
results in standard loop quantum cosmology. We show that the volume remains
non-zero and finite in finite time evolution for all considered loop
cosmological models. Interestingly, even though expansion scalar and energy
density are bounded due to quantum geometry, curvature invariants can still
potentially diverge due to pressure singularities at a finite volume. These
divergences are shown to be harmless since geodesic evolution does not break
down and no strong singularities are present in the effective spacetimes of
loop cosmologies. Using a phenomenological matter model, various types of
exotic strong and weak singularities, including big rip, sudden, big freeze and
type-IV singularities, are studied. We show that as in standard loop quantum
cosmology, big rip and big freeze singularities are resolved in mLQC-I and
mLQC-II, but quantum geometric effects do not resolve sudden and type-IV
singularities.
