Renormalization Group for Non-minimal ${\varphi }^{2}R$ Couplings and Gravitational Contact Interactions

Abstract

Theories of scalars and gravity, with an Einstein-Hilbert term and non-minimal interactions, $M^{2}R/2-\alpha {\varphi }^{2}R/12$, have graviton exchange induced contact interactions. These modify the renormalization group, leading to a discrepancy between the conventional calculations in the Jordan frame that ignore this effect (and are found to be incorrect), and the Einstein frame in which $\alpha$ does not exist. Thus, the calculation of quantum effects in the Jordan and Einstein frames does not generally commute with the transition from the Jordan to the Einstein frame. In the Einstein frame, though $\alpha$ is absent, for small steps in scale $\delta \mu /\mu$ infinitesimal contact terms $\sim \delta \alpha$ are induced, that are then absorbed back into other couplings by the contact terms. This modifies the $\beta$-functions in the Einstein frame. We show how correct results can be obtained in a simple model by including this effect.

11 pages, 4 figures. arXiv admin note: text overlap with arXiv:2009.14782

References in corpus (8)

• Cosmology and the Fate of Dilatation Symmetry
• Quantum scale invariance, cosmological constant and hierarchy problem
• Renormalization group improved gravitational actions: a Brans-Dicke approach
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• On the geometrical interpretation of scale-invariant models of inflation
• Two-loop scale-invariant scalar potential and quantum effective operators
• Axion Induced Oscillating Electric Dipole Moments

Cited by in corpus (6)

• Cosmological implications of the Weyl geometric gravity theory
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Big Bang Nucleosynthesis constraints on the cosmological evolution in a Universe with a Weylian Boundary
• Observational tests of the conformal osculating Barthel-Kropina cosmological model
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• The Weyl Geometric Gravity black hole in light of the Solar System tests