Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field

Abstract

We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing gauge invariant perturbation theory for nonminimally coupled inflationary models.

21 pages, references added, typos corrected, extended section IV on Higgs inflation

References in corpus (8)

• The Standard Model Higgs boson as the inflaton
• Inflation scenario via the Standard Model Higgs boson and LHC
• Power-counting and the Validity of the Classical Approximation During Inflation
• On Inflation with Non-minimal Coupling
• On the one loop corrections to inflation and the CMB anisotropies
• Conformal Transformations with Multiple Scalar Fields
• Quantum radiative corrections to slow-roll inflation
• Path Integral for Inflationary Perturbations

Cited by in corpus (13)

• Equivalence of the Einstein and Jordan frames
• Higgs inflation with loop corrections in the Palatini formulation
• Invariant quantities in the scalar-tensor theories of gravitation
• Higgs inflation and teleparallel gravity
• Critical point Higgs inflation in the Palatini formulation
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Non-Gaussianities of Single Field Inflation with Non-minimal Coupling
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• Note on stability in conformally connected frames
• Naturalness in Higgs inflation in a frame independent formalism
• Manifestly Gauge Invariant Perturbations of Scalar-Tensor Theories of Gravity
• CMB power spectrum for emergent scenario and slow expansion in scalar-tensor theory of gravity
• Nonminimal coupling and the cosmological constant problem