Friedmann Equation of First Order Holonomy Corrections in Loop Quantum Cosmology

The Friedmann equation in Loop Quantum Cosmology (LQC) owns a very different scenario comparing to the classical Friedmann equation with a ρ 2 modified term. Higher order holonomy corrections in LQC has some new property in critical density and inflation, giving us a well-motivated extension. We get a modified Friedmann equation with selecting the first one in higher order holonomy corrections, and show up a new critical density ρ c . From this equation we find some differences in the whole universal evolution, especially in super-inflation and inflation.