Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini

Abstract

We study models of quartic inflation where the inflaton field $\varphi$ is coupled non-minimally to gravity, $\xi {\varphi }^{2}R$, and perform a study of quantum corrections in curved space-time at one-loop level. We specifically focus on comparing results between the metric and Palatini theories of gravity. Transformation from the Jordan to the Einstein frame gives different results for the two formulations and by using an effective field theory expansion we derive the appropriate $\beta$-functions and the renormalisation group improved effective potentials in curved space for both cases in the Einstein frame. In particular, we show that in both formalisms the Einstein frame depends on the order of perturbation theory but that the flatness of the potential is unaltered by quantum corrections.

16 pages, citations added, to appear in JCAP

References in corpus (24)

• The Standard Model Higgs boson as the inflaton
• Primordial Black Holes as Dark Matter
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Higgs inflation: consistency and generalisations
• Power-counting and the Validity of the Classical Approximation During Inflation
• Primordial black hole dark matter from single field inflation
• Primordial Black Holes and Slow-Roll Violation
• On Inflation with Non-minimal Coupling
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Higgs inflation at the critical point
• Higgs inflation still alive
• On the one loop corrections to inflation and the CMB anisotropies
• Spacetime curvature and the Higgs stability during inflation
• Higgs-Palatini Inflation and Unitarity
• Higgs inflation from Standard Model criticality
• Higgs inflation with loop corrections in the Palatini formulation
• Why should we care about the top quark Yukawa coupling?
• On the One Loop Corrections to Inflation II: The Consistency Relation
• Resurrecting Quadratic Inflation with a non-minimal coupling to gravity
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• How (Not) to Palatini
• Quantum radiative corrections to slow-roll inflation
• Is Higgs Inflation Dead?
• Quantum corrections to inflation: the importance of RG-running and choosing the optimal RG-scale

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• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
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• Higgs inflation in metric and Palatini formalisms: Required suppression of higher dimensional operators
• Palatini $R^2$ Quintessential Inflation
• Tachyonic Preheating in Palatini $R^2$ Inflation
• Towards distinguishing variants of non-minimal inflation
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• Implications of Palatini gravity for inflation and beyond
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• Gravitational dark matter production in Palatini preheating
• Non-minimally coupled quartic inflation with Coleman-Weinberg one-loop corrections in the Palatini formulation
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• Slow-roll inflation in Palatini $F(R)$ gravity
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• Inflation and Reheating in f(R,h) theory formulated in the Palatini formalism
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• Non-minimal (self-)running inflation: metric vs. Palatini formulation
• New class of hybrid metric-Palatini scalar-tensor theories of gravity
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Multiple point criticality principle and Coleman-Weinberg inflation
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• Extended interactions in the Palatini-$R^2$ inflation
• Constant-Roll Inflation in modified $f(R,\varphi )$ gravity model using Palatini Formalism
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
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• Einstein-Proca theory from the Einstein-Cartan formulation
• Constraining Palatini-Horndeski theory with gravitational waves after GW170817
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Quintessential Inflation in Palatini Gravity
• Beyond (and back to) Palatini quadratic gravity and inflation
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• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity