Hamilton-Jacobi formalism for inflation with non-minimal derivative coupling

Abstract

In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and lengthy perturbation investigation. In this work we bypass this problem by performing a Hamilton-Jacobi analysis, namely rewriting the cosmological equations considering the scalar field to be the time variable. We apply the method to two specific models, namely the power-law and the exponential cases, and for each model we calculate various observables such as the tensor-to-scalar ratio, and the spectral index and its running. We compare them with 2013 and 2015 Planck data, and we show that they are in a very good agreement with observations.

19 pages, 6 figures, version published in JCAP

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• Constant-roll approach to non-canonical inflation
• Brane Constant-roll Inflation
• Inflation and Acceleration of the Universe by Nonlinear Magnetic Monopole Fields
• Warm Tachyon Inflation and Swampland Criteria
• Cosmological models in modified gravity theories with extended nonminimal derivative couplings
• Beta-function formalism for k-essence constant-roll inflation
• Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation
• Viscous Warm Inflation: Hamilton-Jacobi formalism
• Successful Higgs inflation from combined nonminimal and derivative couplings
• Observational constraints on DBI constant-roll inflation
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Cosmology with variable $G$ and nonlinear electrodynamics
• Hamilton-Jacobi approach for quasi-exponential inflation: predictions and constraints after Planck 2015 results
• Observational constraints on warm quasi-exponential inflation
• General Einstein-Cartan quadratic gravity with derivative couplings
• Constant-roll inflation driven by a scalar field with non-minimal derivative coupling
• Schwinger-Keldysh mechanism in extended quasi single field inflation
• Hamilton-Jacobi formalism for k-inflation
• Derivative coupling of inflaton to $R^{(3)}$
• Frame-Dependence of the Hamilton-Jacobi Formalism for Inflation and Reheating in Non-Minimal Gravity
• Non-canonical scalar field in low anisotropy universe with intermediate inflation
• Reconstructing square-law k-inflation from Planck data