Comoving curvature perturbation in Jordan and Einstein frames

Abstract

In the context of $F(\varphi )R$ models of gravity, the conformal invariance of the curvature perturbation on uniform-field slices has been already demonstrated in several publications. In this work we study the curvature perturbation $\mathcal{R}$ defined on hypersurfaces that comove with the effective fluid whose energy-momentum tensor is covariantly conserved. We derive the expressions of $\mathcal{R}$ at first order in perturbations in the Jordan and Einstein frames and relate the two. Generically $\mathcal{R}$ is not conformally invariant, but it is on sufficiently large scales during slow-roll inflation. Using our results we also rederive the expressions for inflation observables in the Jordan frame.

arXiv comment23 pages

References in corpus (27)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Modified Gravity and Cosmology
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The Standard Model Higgs boson as the inflaton
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• A general proof of the conservation of the curvature perturbation
• Formalising the Slow-Roll Approximation in Inflation
• Cosmological perturbations
• The conformal frame freedom in theories of gravitation
• Adiabatic Modes in Cosmology
• Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
• Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory
• Cosmological Perturbations with Multiple Fluids and Fields
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Extended Slow-Roll Conditions and Rapid-Roll Conditions
• Conformal invariance of curvature perturbation
• Imperfect fluid description of modified gravities
• Forming sub-horizon black holes at the end of inflation
• The Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling
• Induced-gravity Inflation and the Density Perturbation Spectrum
• Progress in Higgs inflation
• Constraints in the Context of Induced-gravity Inflation
• Equivalence of cosmological observables in conformally related scalar tensor theories
• Are there really conformal frames? Uniqueness of affine inflation
• Relaxing inflation models with non-minimal coupling: A general study
• Slow-Roll Inflation in the Jordan Frame

Cited by in corpus (5)

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• Imprints of screened dark energy on nonlocal quantum correlations
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• Onset of dark energy from cosmological scalarization and gravitational wave speed
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity