The probability of inflation in Loop Quantum Cosmology

The probability of there being sufficient inflation to solve the fine-tuning associated with the horizon and flatness problems has recently been shown to be exponentially small, within the context of classical general relativity. Here this result is extended by considering loop quantum gravity effects, that are significant at small scales. In addition to accounting for high-energy departures from classicality, it is shown that, in contrast to the classical case, the loop quantum cosmological probability measure is naturally finite, at least in some well defined region. It is also shown that these loop quantum gravity corrections can overcome the classical suppression of the probability only for extremely unnatural choices of ambiguity parameters, implying that single field, slow-roll inflation is exponentially unlikely.