Measures in Mutlifield Inflation

Abstract

We examine the classical dynamics of multifield inflation models with quadratic potentials. Such models are shown to have inflationary attractors in phase space, consistent with the stretching of phase space trajectories along the volume factor of the universe during inflation. Using the symplectic structure associated with Hamiltonian systems we form a measure on the phase space, as initially proposed by Gibbons, Hawking and Stewart. This is used to calculate lower bounds on the probabilities of observational agreement (i.e. the probability the model gives a value for the spectral index within the region $n_s=0.968\pm 0.006$) for equal mass two and three field models with quadratic potentials, giving values of 0.982 and 0.997 respectively. We derive the measure for a general $N$-field model and argue that as the number of fields approaches infinity, the probability of observational agreement approaches one.

arXiv comment16 pages, 3 figures

References in corpus (15)

• Inflation Dynamics and Reheating
• Flux Compactification
• The Measure Problem in Cosmology
• Non-Gaussianities in Multi-field Inflation
• Probability of Inflation in Loop Quantum Cosmology
• Loop quantum cosmology and slow roll inflation
• Measure and Probability in Cosmology
• On the measure problem in slow roll inflation and loop quantum cosmology
• Attractor Solutions in Scalar-Field Cosmology
• Simple predictions from multifield inflationary models
• How Many $e$-Folds Should We Expect from High-Scale Inflation?
• MultiModeCode: An efficient numerical solver for multifield inflation
• Inflationary Attractors and their Measures
• The Hubble Slow Roll Expansion for Multi Field Inflation
• Minimal Coupling and Attractors

Cited by in corpus (1)

• Inflationary $\alpha$-attractor cosmology: A global dynamical systems perspective