Frame independent cosmological perturbations

Abstract

We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and $n$-point functions.

29 pages

References in corpus (12)

• The Standard Model Higgs boson as the inflaton
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Higgs inflation: consistency and generalisations
• On Inflation with Non-minimal Coupling
• On the one loop corrections to inflation and the CMB anisotropies
• A note on the role of the boundary terms for the non-Gaussianity in general k-inflation
• Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
• The Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling
• Path Integral for Inflationary Perturbations
• Non-Gaussianities of Single Field Inflation with Non-minimal Coupling
• Uniqueness of the gauge invariant action for cosmological perturbations
• Gauge invariance and non-Gaussianity in Inflation

Cited by in corpus (30)

• Question of quantum equivalence between Jordan frame and Einstein frame
• Equivalence of the Einstein and Jordan frames
• Invariant quantities in the scalar-tensor theories of gravitation
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• New universal attractor in nonmininally coupled gravity: Linear inflation
• Quantum corrections in Higgs inflation: the real scalar case
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• UV (in)sensitivity of Higgs inflation
• Gauge-invariant quantum gravitational corrections to correlation functions
• Scalar-tensor linear inflation
• Non-minimal (self-)running inflation: metric vs. Palatini formulation
• Reconstruction of extended inflationary potentials for attractors
• Multiple point criticality principle and Coleman-Weinberg inflation
• On the number of $e$-folds in the Jordan and Einstein frames
• Generating scale-invariant tensor perturbations in the non-inflationary universe
• On the Decoherence of Primordial Gravitons
• Effect of transitions in the Planck mass during inflation on primordial power spectra
• Non-minimally coupled curvaton
• Slow-Roll Inflation in the Jordan Frame
• Note on stability in conformally connected frames
• Higgs field in cosmology
• Constraints on non-minimal coupling from quantum cosmology
• Perturbative reduction of derivative order in EFT
• Entropy production in inflation from spectator loops
• Inflation from cosmological constant and nonminimally coupled scalar
• Synchronous coordinates and gauge-invariant observables in cosmological spacetimes
• Einstein and Jordan frame correspondence in quantum cosmology: Expansion-collapse duality
• Conformal invariant cosmological perturbations via the covariant approach
• Bouncing and collapsing universes dual to late-time cosmological models
• Conformal invariant cosmological perturbations via the covariant approach: multicomponent universe