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.

arXiv comment21 pages, references added, typos corrected, extended section IV on Higgs inflation

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Cited by in corpus (35)

• Modified Gravity and Cosmology
• Higgs inflation
• 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
• Planck scale black hole dark matter from Higgs inflation
• Higgs inflation with the Holst and the Nieh-Yan term
• Higgs inflation in the Palatini formulation with kinetic terms for the metric
• Higgs inflation at the hilltop
• Quantum corrections in Higgs inflation: the real scalar case
• UV (in)sensitivity of Higgs inflation
• Higgs inflation and teleparallel gravity
• Critical point Higgs inflation in the Palatini formulation
• Frame independent cosmological perturbations
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Higgs-$R^2$ inflation -- full slow-roll study at tree-level
• Non-Gaussianities of Single Field Inflation with Non-minimal Coupling
• Reconstruction of a Nonminimal Coupling Theory with Scale-invariant Power Spectrum
• Uniqueness of the gauge invariant action for cosmological perturbations
• Reconstruction of extended inflationary potentials for attractors
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• Note on stability in conformally connected frames
• Quantum gravitational corrections from the Wheeler-DeWitt equation for scalar-tensor theories
• Constraints on non-minimal coupling from quantum cosmology
• The role of conformal symmetry in gravity and the standard model
• Naturalness in Higgs inflation in a frame independent formalism
• Manifestly Gauge Invariant Perturbations of Scalar-Tensor Theories of Gravity
• Higgs Inflation in f(Φ,R) Theory
• Entropy production in inflation from spectator loops
• Inflation from cosmological constant and nonminimally coupled scalar
• Gauge Invariant Perturbation Theory via Homotopy Transfer
• Testing theories of Gravity and Supergravity with inflation and observations of the cosmic microwave background
• One loop corrected conformally coupled scalar mode equations during inflation
• CMB power spectrum for emergent scenario and slow expansion in scalar-tensor theory of gravity
• Nonminimal coupling and the cosmological constant problem