Inflationary Attractors and their Measures
  Several recent misconceptions about the measure problem in inflation and the
nature of inflationary attractors are addressed. We show that within the
Hamiltonian system of flat Friedmann-Lema\^itre-Robertson-Walker cosmology
coupled to a massive scalar field, the focussing of the Liouville measure on
attractor solutions is brought about by a spread in a gauge degree of freedom -
the spatial volume. Using this we show how the Liouville measure formulated on
a surface of constant Hubble rate induces a probability distribution function
on surfaces of other Hubble rates, and the attractor behaviour is seen through
the focussing of this function on a narrow range of physical observables. One
can conclude then that standard techniques from Hamiltonian dynamics suffice to
provide a satisfactory description of attractor solutions and the measure
problem.
  Updated to match published version.
