Genericness of pre-inflationary dynamics and probability of the desired
  slow-roll inflation in modified loop quantum cosmologies
  We study the evolution of spatially flat
Friedmann-Lema\^{i}tre-Robertson-Walker universe for chaotic and Starobinsky
potentials in the framework of modified loop quantum cosmologies. These models
result in a non-singular bounce as in loop quantum cosmology, but with far more
complex modified Friedmann dynamics with higher order than quadratic terms in
energy density. For the kinetic energy dominated bounce, we obtain analytical
solutions using different approximations and compare with numerical evolution
for various physical variables. The relative error turns out to be less than
$0.3\%$ in the bounce regime for both of the potentials. Generic features of
dynamics, shared with loop quantum cosmology, are established using analytical
and numerical solutions. Detailed properties of three distinct phases in
dynamics separating bounce regime, transition stage and inflationary phase are
studied. For the potential energy dominated bounce, we qualitatively describe
its generic features and confirm by simulations that they all lead to the
desired slow-roll phase in the chaotic inflation. However, in the Starobinsky
potential, the potential energy dominated bounce cannot give rise to any
inflationary phase. Finally, we compute the probability for the desired
slow-roll inflation to occur in the chaotic inflation and as in loop quantum
cosmology, find a very large probability for the universe to undergo inflation.
