Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 31, Issue 6, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/31/6/062001
Keywords
inflationary dynamics; attractors; measure problem
Categories
Funding
- CONACyT [0177840]
- DGAPA-UNAM [IN100212]
- Templeton Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [1205388] Funding Source: National Science Foundation
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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.
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