[Paper Review] A Revision to the Issue of Frames by Non-minimal Large Field Inflation

Mehdi Shokri|arXiv (Cornell University)|Oct 13, 2017

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper investigates non-minimally coupled large field inflation models in Jordan and Einstein frames via conformal transformation, comparing slow-roll parameters and observational constraints. It finds that for chaotic inflation, the Einstein frame is physically preferred, while for power-law potentials, the Jordan frame is more consistent with data, suggesting frame dependence in quantum-corrected scenarios.

ABSTRACT

We present an extended study of inflationary models that inflaton field is non-minimally coupled with gravity. We study parameters space of the models up to the second (and in some cases third) order of the slow-roll parameters for usual large field potentials in Jordan and Einstein frames that are connected each other by conformal transformation. We calculate inflationary parameters and the results are compared in both frames and also with observations. By using the recent observational datasets, we present a discussion in order to clarify the physical frame between Jordan and Einstein frames. Also, some suggestions are expressed in order to navigate us for the future works.

Motivation & Objective

• To resolve the long-standing debate on physical frame equivalence between Jordan and Einstein frames in non-minimal inflation.
• To analyze slow-roll parameters for standard large field potentials (chaotic and power-law) in both frames using conformal transformation.
• To compare theoretical predictions with recent observational data (e.g., Planck) to determine which frame yields physically consistent results.
• To explore the role of quantum corrections in breaking frame equivalence, proposing future directions in non-commutative cosmology and Finsler geometry.
• To clarify whether physical equivalence between frames holds under quantum gravitational effects, especially in non-minimal coupling scenarios.

Proposed method

• Formalism based on the action with non-minimal coupling term $\frac{1}{2}\xi R\varphi^2$, where $\xi$ is the coupling constant.
• Application of conformal transformation $\hat{g}_{\mu\nu} = \Omega g_{\mu\nu}$ with $\Omega = \Omega(\varphi)$ to map Jordan frame to Einstein frame.
• Derivation of slow-roll parameters $\epsilon$, $\eta$, and $n_s$ up to second (and third) order in both frames for two large field potentials.
• Comparison of inflationary predictions (scalar spectral index $n_s$, tensor-to-scalar ratio $r$) with Planck 2015 and other observational datasets.
• Use of observational constraints to assess physical viability of each frame for different potential types.
• Proposal of quantum-corrected frameworks: non-commutative mini-superspace deformation and Finsler geometry as alternatives to Riemannian GR for future frame analysis.

Experimental results

Research questions

• RQ1 Does the physical equivalence between Jordan and Einstein frames hold when quantum corrections are considered in non-minimal inflation?
• RQ2 For which class of large field potentials (chaotic vs. power-law) is the Einstein frame more consistent with observational data?
• RQ3 How do slow-roll parameters differ between frames, and what are the implications for inflationary model selection?
• RQ4 Can non-commutative cosmology or Finsler geometry provide a framework to resolve the frame ambiguity in quantum gravity?
• RQ5 What role does the non-minimal coupling constant $\xi$ play in breaking frame equivalence under quantum corrections?

Key findings

• For the chaotic inflation potential ($V(\varphi) \propto \varphi^2$) with $m \ll \beta$, deviations in inflationary parameters are observed between Jordan and Einstein frames.
• The Einstein frame yields better agreement with Planck observations for the chaotic potential, suggesting it is the physically preferred frame in this case.
• For the power-law potential ($V(\varphi) \propto \varphi^n$), no significant deviation is found between frames, and the Jordan frame is more consistent with data.
• The study concludes that frame preference is not universal but depends on the form of the inflaton potential.
• Quantum corrections are expected to break frame equivalence, indicating that physical frame selection cannot be assumed a priori.
• The paper proposes non-commutative cosmology and Finsler geometry as promising avenues for future research to resolve the frame ambiguity in quantum gravity.