Meaning of the field dependence of the renormalization scale in Higgs inflation

Abstract

We consider the prescription dependence of the Higgs effective potential under the presence of general nonminimal couplings. We evaluate the fermion loop correction to the effective action in a simplified Higgs-Yukawa model whose path integral measure takes simple form either in the Jordan or Einstein frame. The resultant effective action becomes identical in both cases when we properly take into account the quartically divergent term coming from the change of measure. Working in the counterterm formalism, we clarify that the difference between the prescriptions I and II comes from the counter term to cancel the logarithmic divergence. This difference can be absorbed into the choice of tree-level potential from the infinitely many possibilities, including all the higher-dimensional terms. We also present another mechanism to obtain a flat potential by freezing the running of the effective quartic coupling for large field values, using the nonminimal coupling in the gauge kinetic function.

19 pages; version to appear in Phys. Rev. D; title changed according to editor's request; paragraphs added in the end of Secs. 3.3 and 4; minor modifications

References in corpus (10)

• The Standard Model Higgs boson as the inflaton
• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Higgs inflation at the critical point
• Higgs inflation still alive
• Equivalence of the Einstein and Jordan frames
• Higgs inflation from Standard Model criticality
• Violent Preheating in Inflation with Nonminimal Coupling
• Inflation by non-minimal coupling
• Conformal frames in cosmology
• Plateau Inflation from Random Non-Minimal Coupling

Cited by in corpus (26)

• Higgs inflation with loop corrections in the Palatini formulation
• Planck scale black hole dark matter from Higgs inflation
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Higgs inflation in the Palatini formulation with kinetic terms for the metric
• New universal attractor in nonmininally coupled gravity: Linear inflation
• Higgs inflation at the hilltop
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Critical point Higgs inflation in the Palatini formulation
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• A minimal model of inflation and dark radiation
• The Inflaton that Could : Primordial Black Holes and Second Order Gravitational Waves from Tachyonic Instability induced in Higgs-$R^2$ Inflation
• Progress in Higgs inflation
• Non-minimal (self-)running inflation: metric vs. Palatini formulation
• On Preheating in Higgs Inflation
• Hybrid Higgs Inflation: The Use of Disformal Transformation
• Asymptotic Scale Invariance and its Consequences
• Hidden and explicit quantum scale invariance
• Quartic inflation and radiative corrections with non-minimal coupling
• Cosmological implications of Standard Model criticality and Higgs inflation
• Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory
• Thermal Loop Effects on Large-Scale Curvature Perturbation in the Higgs Inflation
• No-scale Brans-Dicke Gravity -- ultralight scalar boson & heavy inflaton
• Minimal scenario of Criticality for Electroweak scale, Neutrino Masses, Dark Matter, and Inflation
• Robustness of predicted CMB fluctuations in Cartan $F(R)$ gravity
• Hill-climbing dark inflation
• Dynamical dark energy in the no-scale Brans-Dicke gravity