On the measure problem in slow roll inflation and loop quantum cosmology

TL;DR

This paper investigates the measure problem in slow-roll inflation within loop quantum cosmology, revealing that the probability of sufficient inflation approaches one as the theory transitions to classical general relativity, and clarifies discrepancies with previous results.

Contribution

It demonstrates that in loop quantum cosmology, the probability of enough inflation increases towards unity near the classical limit and explains the origin of conflicting results in prior studies.

Findings

Probability of sufficient inflation approaches 1 near the GR limit in LQC.

Initial condition choices significantly affect inflation probability calculations.

Loop quantum cosmology naturally favors initial conditions leading to sufficient inflation.

Abstract

We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to one in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.