Frame-dependence of higher-order inflationary observables in scalar-tensor theories

Abstract

In the context of scalar-tensor theories of gravity we compute the third-order corrected spectral indices in the slow-roll approximation. The calculation is carried out by employing the Green's function method for scalar and tensor perturbations in both the Einstein and Jordan frames. Then, using the interrelations between the Hubble slow-roll parameters in the two frames we find that the frames are equivalent up to third order. Since the Hubble slow-roll parameters are related to the potential slow-roll parameters, we express the observables in terms of the latter which are manifestly invariant. Nevertheless, the same inflaton excursion leads to different predictions in the two frames since the definition of the number of e-folds differs. To illustrate this effect we consider a nonminimal inflationary model and find that the difference in the predictions grows with the nonminimal coupling and it can actually be larger than the difference between the first and third order results for the observables. Finally, we demonstrate the effect of various end-of-inflation conditions on the observables. These effects will become important for the analyses of inflationary models in view of the improved sensitivity of future experiments.

Title changed per journal request, typos fixed, a few comments and references added, to appear in PRD

References in corpus (41)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Standard Model Higgs boson as the inflaton
• A Joint Analysis of BICEP2/Keck Array and Planck Data
• Higgs inflation: consistency and generalisations
• The Unity of Cosmological Attractors
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Scale invariance, unimodular gravity and dark energy
• Higgs inflation at the critical point
• Higgs inflation still alive
• Large Field Inflation and Double $\alpha$-Attractors
• Equivalence of the Einstein and Jordan frames
• Inflationary universe from perfect fluid and $F(R)$ gravity and its comparison with observational data
• Planck, LHC, and $\alpha$-attractors
• Higgs inflation from Standard Model criticality
• Single-field $\alpha$-attractors
• Physical non-equivalence of the Jordan and Einstein frames
• Invariant quantities in the scalar-tensor theories of gravitation
• A Unitarity-Conserving Higgs Inflation Model
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Inflationary $\alpha$-attractors from $F(R)$ Gravity
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• On the geometrical interpretation of scale-invariant models of inflation
• Embedding inflation into the Standard Model - more evidence for classical scale invariance
• Inflation from Broken Scale Invariance
• Inflation by non-minimal coupling
• The double attractor behavior of induced inflation
• K-inflationary Power Spectra in the Uniform Approximation
• Frame Covariant Nonminimal Multifield Inflation
• Reconstructing the inflationary $f(R)$ from observations
• Non-Minimal Inflation after WMAP3
• Inflation and reheating in scale-invariant scalar-tensor gravity
• Nonminimal coupling and inflationary attractors
• Non-Minimal Two-Loop Inflation
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• Power spectra and spectral indices of $k$-inflation: high-order corrections
• Gravitational wave astronomy: the definitive test for the "Einstein frame versus Jordan frame" controversy
• Power Spectrum of Inflationary Attractors
• Perturbations of Single-field Inflation in Modified Gravity Theory
• Equivalence of Einstein and Jordan frames in quantized cosmological models
• Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method
• The observational position of simple non-minimally coupled inflationary scenarios

Cited by in corpus (36)

• Selected topics in scalar-tensor theories and beyond
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Palatini $R^2$ Quintessential Inflation
• Quintessential inflation: A tale of emergent and broken symmetries
• $R^p$ Attractors Static Neutron Star Phenomenology
• Universal Inflationary Attractors Implications on Static Neutron Stars
• Inflationary Attractors Predictions for Static Neutron Stars in the Mass-Gap Region
• Static Neutron Stars Perspective of Quadratic and Induced Inflationary Attractor Scalar-tensor Theories
• Slow-Roll Inflation at N3LO
• On the number of $e$-folds in the Jordan and Einstein frames
• Metric-affine gravity effects on terrestrial (exo-)planets profiles
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• Slow-Roll Inflation in the Jordan Frame
• Primordial power spectrum at N3LO in effective theories of inflation
• Note on stability in conformally connected frames
• Post-Newtonian parameters $\gamma$ and $\beta$ of scalar-tensor gravity for a homogeneous gravitating sphere
• Formalizing Slow-roll Inflation in Scalar-Tensor Theories of Gravitation
• Generalized $R^p$-attractor Cosmology in the Jordan and Einstein Frames: New Type of Attractors and Revisiting Standard Jordan Frame $R^p$ Inflation
• Scale Invariant Gravity and Black Hole Ringdown
• Renormalization Group for Non-minimal ${\varphi }^{2}R$ Couplings and Gravitational Contact Interactions
• Comparing geometric and gravitational particle production in Jordan and Einstein frames
• Imprints of screened dark energy on nonlocal quantum correlations
• Global Portraits of Nonminimal Inflation: Metric and Palatini
• Comoving curvature perturbation in Jordan and Einstein frames
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections
• Clocking the End of Cosmic Inflation
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
• Fifth forces and frame invariance
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• Ward identities under the frame transformations in curved spacetime