The Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling

Abstract

The method of a conformal transformation is applied to a general class of single field inflation models with non-minimal coupling to gravity and non-standard kinetic terms, in order to reduce the cosmological perturbative calculation to the conventional minimal coupling case to all orders in perturbation theory. Our analysis is made simple by the fact that all perturbation variables in the comoving gauge are conformally invariant to all orders. The structure of the vacuum, on which cosmological correlation functions are evaluated, is also discussed. We show how quantization in the Jordan frame for non-minimally coupled inflation models can be equivalently implemented in the Einstein frame. It is thereafter argued that the general N-point cosmological correlation functions (of the curvature perturbation) are independent of the conformal frame.

15 pages, no figure, references added

References in corpus (10)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Higgs G-inflation
• Primordial non-Gaussianities in general modified gravitational models of inflation
• Non-gaussianity from the trispectrum in general single field inflation
• Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model
• Primordial non-Gaussianity from G-inflation
• Inflation with General Initial Conditions for Scalar Perturbations
• Inflation by non-minimal coupling
• Non-Gaussianities of Single Field Inflation with Non-minimal Coupling

Cited by in corpus (33)

• Question of quantum equivalence between Jordan frame and Einstein frame
• Equivalence of the Einstein and Jordan frames
• Higgs inflation from Standard Model criticality
• Higgs inflation with loop corrections in the Palatini formulation
• Invariant quantities in the scalar-tensor theories of gravitation
• Higgs inflation at the hilltop
• UV (in)sensitivity of Higgs inflation
• Probing reheating with primordial spectrum
• Curvature perturbation in multi-field inflation with non-minimal coupling
• Frame independent cosmological perturbations
• Uniqueness of the gauge invariant action for cosmological perturbations
• Reconstruction of extended inflationary potentials for attractors
• Generating scale-invariant tensor perturbations in the non-inflationary universe
• The slow expansion with nonminimal derivative coupling and its conformal dual
• A Non-minimally Coupled Potential for Inflation and Dark Energy after Planck 2015: A Comprehensive Study
• Slow-Roll Inflation in the Jordan Frame
• Natural Inflation with non minimal coupling to gravity in $R^2$ gravity under the Palatini formalism
• Note on stability in conformally connected frames
• Adiabatic regularisation of power spectra in $k$-inflation
• Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation
• Comparing geometric and gravitational particle production in Jordan and Einstein frames
• Adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation
• Adiabatic regularisation of power spectra in nonminimally coupled chaotic inflation
• Superpotential method and the amplification of inflationary perturbations
• Comoving curvature perturbation in Jordan and Einstein frames
• Conformal invariant cosmological perturbations via the covariant approach
• Effects of Variable Newton Constant During Inflation
• On non-minimal coupling of the inflaton
• On the Disformal Transformation of the Einstein-Hilbert Action
• Energy momentum tensor of a non-minimally coupled scalar from the equivalence of the Einstein and Jordan frames
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity
• Modified Power law Inflation: solution to the graceful exit problem and improvement of dark energy models
• Conformal invariant cosmological perturbations via the covariant approach: multicomponent universe