Analytical approximation techniques in background loop quantum cosmology

Abstract

In this report we present analytical approximation techniques to describe how a scalar field with an arbitrary potential evolves in the background of a quantum FLRW spacetime described by LQC. In general there is an initial phase of superinflation independent of the shape of the potential, then there is a damping phase which leads to turnaround and then finally we have a phase of slow-roll inflation. The percentage error between the values of observables (like scalar field $\phi$ and its derivative $\dot{\phi}$) predicted by the analytic and numerical data are in general less than 5 percent and this is shown in tables. These analytical techniques work very well for all cases of the potentials (quadratic, Starobinsky and quartic) we have considered here except for the potential energy dominated regime of the Starobinsky potential. The reason is that due to the nature of the regime there we have to use damping equations several times to reach the bottom of the potential where the next regime starts which makes it infeasible. Thus we propose an alternate way of analytically understanding that regime which agrees with the numerical results