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We study the evolution of spatially flatFriedmann-Lema\^{i}tre-Robertson-Walker universe for chaotic and Starobinskypotentials in the framework of modified loop quantum cosmologies. These modelsresult in a non-singular bounce as in loop quantum cosmology, but with far morecomplex modified Friedmann dynamics with higher order than quadratic terms inenergy density. For the kinetic energy dominated bounce, we obtain analyticalsolutions using different approximations and compare with numerical evolutionfor 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 ofdynamics, shared with loop quantum cosmology, are established using analyticaland numerical solutions. Detailed properties of three distinct phases indynamics separating bounce regime, transition stage and inflationary phase arestudied. For the potential energy dominated bounce, we qualitatively describeits generic features and confirm by simulations that they all lead to thedesired slow-roll phase in the chaotic inflation. However, in the Starobinskypotential, the potential energy dominated bounce cannot give rise to anyinflationary phase. Finally, we compute the probability for the desiredslow-roll inflation to occur in the chaotic inflation and as in loop quantumcosmology, find a very large probability for the universe to undergo inflation.

Genericness of pre-inflationary dynamics and probability of the desired slow-roll inflation in modified loop quantum cosmologies