Type: Article

Inflationary attractors and their measures

Corichi, Alejandro; Sloan, David;

Abstract:

Several recent misconceptions about the measure problem in inflation and the nature of inflationary attractors are addressed. We clarify some issues regarding the Hamiltonian dynamics of a flat Friedmann-Lemaitre-Robertson-Walker cosmology coupled to a massive scalar field. In particular we show that the focusing of the Liouville measure on attractor solutions is recovered by properly dealing with a gauge degree of freedom related to the rescaling of the spatial volume. Furthermore, we show how the Liouville measure formulated on a surface of constant Hubble rate, together with the assumption of constant a priory probability, induces a non-uniform probability distribution function on any other surfaces of other Hubble rates. The attractor behaviour is seen through the focusing of this function on a narrow range of physical observables. This qualitative behaviour is robust under change of potential and underlying measure. One can then conclude that standard techniques from Hamiltonian dynamics suffice to provide a satisfactory description of attractor solutions and the measure problem for inflationary dynamics.