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We study the evolution of a spatially flat Friedmann-Lemaître-Robertson-Walker universe for chaotic and Starobinsky potentials in the framework of modified loop quantum cosmologies. These models result in a nonsingular bounce as in loop quantum cosmology, but with far more complex modified Friedmann dynamics with higher order than quadratic terms in the 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. The generic features of the dynamics - shared with loop quantum cosmology - are established using analytical and numerical solutions. The detailed properties of the three distinct phases in the dynamics separating the bounce regime, transition stage, and inflationary phase are studied. We qualitatively describe the generic features of the potential-energy-dominated bounce 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 an 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.

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Physical Review D