Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models

Abstract

Single-field inflaton models in the kinetic dominance period admit formal solutions given by generalized asymptotic expansions called psi series. We present a method for computing psi series for the Hubble parameter as a function of the inflaton field in the Hamilton-Jacobi formulation of inflaton models. Similar psi series for the scale factor, the conformal time and the Hubble radius are also derived. They are applied to determine the value of the inflaton field when the inflation period starts and to estimate the contribution of the kinetic dominance period to calculate the duration of inflation. These psi series are also used to obtain explicit two-term truncated psi series near the singularity for the potentials of the Mukhanov-Sasaki equation for curvature and tensor perturbations. The method is illustrated with wide families of inflaton models determined by potential functions combining polynomial and exponential functions as well as with generalized Starobinsky models.

arXiv comment30 pages, 9 figures

References in corpus (14)

• Inflation Dynamics and Reheating
• Reconstructing the Inflaton Potential --- an Overview
• Formalising the Slow-Roll Approximation in Inflation
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• Inflationary Cosmology
• Closed Universes, de Sitter Space and Inflation
• Kinetic Initial Conditions for Inflation
• The pre-inflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles
• Psi-Series Solution of Fractional Ginzburg-Landau Equation
• The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis
• Constraining the kinetically dominated Universe
• A case for kinetically dominated initial conditions for inflation
• Logolinear series expansions with applications to primordial cosmology
• Separatrices in the Hamilton-Jacobi Formalism of Inflaton Models

Cited by in corpus (4)

• Frame-Dependence of the Hamilton-Jacobi Formalism for Inflation and Reheating in Non-Minimal Gravity
• Kinetic dominance and the wavefunction of the universe
• On the slow roll expansion of one-field cosmological models
• Adaptive asymptotic solutions of inflationary models in the Hamilton-Jacobi formalism: Application to T-models