Inflationary Attractors and their Measures

Abstract

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-Lemaître-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.

8 pages, 1 figure

References in corpus (6)

• Eternal inflation and its implications
• The Measure Problem in Cosmology
• Measure and Probability in Cosmology
• Towards a gauge invariant volume-weighted probability measure for eternal inflation
• On the measure problem in slow roll inflation and loop quantum cosmology
• Attractor Solutions in Scalar-Field Cosmology

Cited by in corpus (35)

• Robustness of Inflation to Inhomogeneous Initial Conditions
• Initial Conditions for Inflation - A Short Review
• Inflation after Planck: Judgment Day
• Robustness of Inflation to Large Tensor Perturbations
• The Degree of Fine-Tuning in our Universe -- and Others
• The Effects of Potential Shape on Inhomogeneous Inflation
• Global dynamics and inflationary center manifold and slow-roll approximants
• Genericness of pre-inflationary dynamics and probability of the desired slow-roll inflation in modified loop quantum cosmologies
• Inflation with the Starobinsky potential in Loop Quantum Cosmology
• Dynamical Similarity
• Loop Quantum Cosmology: A brief review
• Phenomenological implications of modified loop cosmologies: an overview
• Inflating an Inhomogeneous Universe
• Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology
• A New Action for Cosmology
• When scale is surplus
• Quantum gravitational onset of Starobinsky inflation in a closed universe
• Designing and testing inflationary models with Bayesian networks
• Brans--Dicke cosmology does not have the $\Lambda$CDM phase as an universal attractor
• T-Model Inflation and Bouncing Cosmology
• Polymer inflation
• Probability of inflation in Loop Quantum Cosmology
• Minimal Coupling and Attractors
• Robustness of inflation to kinetic inhomogeneities
• Pure shape dynamics: General framework
• Quantum gravity might restrict a cyclic evolution
• Initial Conditions of Inflation in a Bianchi I Universe
• Semiclassical cosmology with back reaction: the Friedmann-Schrodinger equation and inflation
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Volume Weighting the Measure of the Universe from Classical Slow-Roll Expansion
• Modeling the Past Hypothesis: A Mechanical Cosmology
• $w=-1$ as an Attractor
• Alternative effective mass functions in the modified Mukhanov-Sasaki equation of loop quantum cosmology
• Measures in Mutlifield Inflation
• Janus Points and Arrows of Time