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

## TL;DR

This paper investigates the dynamics of modified loop quantum cosmologies with complex Friedmann equations, analyzing conditions for successful slow-roll inflation and finding a high probability for inflation in chaotic models.

## Contribution

It introduces and analyzes a new class of modified loop quantum cosmologies with higher-order energy density terms, exploring their inflationary implications.

## Key findings

- Analytical solutions match numerical results with less than 0.3% error.
- Generic bounce features are similar to standard loop quantum cosmology.
- High probability of desired slow-roll inflation in chaotic models.

## Abstract

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.