Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory

Abstract

\noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easiliy obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase trnasitions), are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. Stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the Standard Model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable.

23 pages, Oct 17 1994

References in corpus (6)

• Leading Quantum Correction to the Newtonian Potential
• The effective potential and the renormalisation group
• Renormalization-group improved effective potential for gauge theories in curved spacetime
• Renormalization-Group Improved Effective Lagrangian for Interacting Theories in Curved Spacetime
• The Dark Matter Problem in Light of Quantum Gravity
• Improving the Effective Potential:Multi-Mass-Scale Case

Cited by in corpus (27)

• Ostrogradski Formalism for Higher-Derivative Scalar Field Theories
• Dimensional Transmutation in Gravity and Cosmology
• Effective action for the Yukawa model in curved spacetime
• Quartic propagators, negative norms and the physical spectrum
• Does Planck really rule out monomial inflation?
• GUTs in Curved Spacetime: Running Gravitational Constants, Newtonian Potential and the Quantum Corrected Gravitational Equations
• Inflationary universe from higher derivative quantum gravity coupled with scalar electrodynamics
• Conformal Symmetry in Field Theory and in Quantum Gravity
• Stability of the effective potential of the gauge-less top-Higgs model in curved spacetime
• Cyclic cosmology in modified gravity
• Cosmological Constant Problem and Renormalized Vacuum Energy Density in Curved Background
• Signs and Stability in Higher-Derivative Gravity
• Electroweak Vacuum Instability and Renormalized Vacuum Field Fluctuations in Friedmann-Lemaitre-Robertson-Walker Background
• Exorcising Ghosts in Induced Gravity
• Gauged Yukawa model in curved spacetime
• Ultraviolet complete dark energy model
• Curved spacetime effective field theory (cEFT) -- construction with the heat kernel method
• First constraints on non-minimally coupled Natural and Coleman-Weinberg inflation and massive neutrino self-interactions with Planck+BICEP/Keck
• Gauge Fixing in Higher Derivative Gravity
• Effective Potential of Scalar-Tensor Gravity
• Nonlinear massive spin-two field generated by higher derivative gravity
• Spontaneous Conformal Symmetry Breaking and Quantum Quadratic Gravity
• Matter scattering in $R_{\mu \nu }^2$ gravity and unitarity
• Perturbative $S$-matrix unitarity ($S^{†}S=1$) in $R_{\mu \nu }^2$ gravity
• High-energy properties of the graviton scattering in quadratic gravity
• Yang-Mills Yukawa model in curved spacetime
• Darkflation -- one scalar to rule them all?