Effective field theory of degenerate higher-order inflation

Abstract

We extend the effective field theory of inflation to a general Lagrangian constructed from Arnowitt-Deser-Misner variables that encompasses the most general interactions with up to second derivatives of the scalar field whose background breaks temporal diffeomorphism invariance. Degeneracy conditions, corresponding to 8 distinct types -- only one of which corresponds to known degenerate higher-order scalar-tensor models -- provide necessary conditions for eliminating the Ostrogradsky ghost in a covariant theory at the level of the quadratic action in unitary gauge. Novel implications of the degenerate higher-order system for the Cauchy problem are illustrated with the phase space portrait of an explicit inflationary example: not all field configurations lead to physical solutions for the metric even for positive potentials; solutions are unique for a given configuration only up to a branch choice; solutions on one branch can apparently end at nonsingular points of the metric and their continuation on alternate branches lead to nonsingular bouncing solutions; unitary gauge perturbations can go unstable even when degenerate terms in the Lagrangian are infinitesimal. The attractor solution leads to an inflationary scenario where slow-roll parameters vary and running of the tilt can be large even with no explicit features in the potential far from the end of inflation, requiring the optimized slow-roll approach for predicting observables.

24 pages, 5 figures; matches published version

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Cited by in corpus (12)

• On Rotating Black Holes in DHOST Theories
• General Relativity solutions with stealth scalar hair in quadratic higher-order scalar-tensor theories
• Invertible disformal transformations with higher derivatives
• Black hole perturbations in DHOST theories: Master variables, gradient instability, and strong coupling
• Generalized Regge-Wheeler Equation from Effective Field Theory of Black Hole Perturbations with a Timelike Scalar Profile
• Stealth dark energy in scordatura DHOST theory
• Invertible disformal transformations with arbitrary higher-order derivatives
• Effective description of generalized disformal theories
• Inflation with $0\le c_{\mathrm{s}}\le 1$
• Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions
• Generalized disformal invariance of cosmological perturbations with second-order field derivatives
• The Black Hole Window on Cosmic Inflation