Abstract
Within the Asymptotic Safety scenario, we discuss whether Quantum Einstein Gravity (QEG) can give rise to a semi-classical regime of propagating physical gravitons (gravitational waves) governed by an effective theory which complies with the standard rules of local quantum field theory. According to earlier investigations based on single-metric truncations there is a tension between this requirement and the condition of Asymptotic Safety since the former (latter) requires a positive (negative) anomalous dimension of Newton's constant. We show that the problem disappears using the bi-metric renormalization group flows that became available recently: They admit an asymptotically safe UV limit and, at the same time, a genuine semi-classical regime with a positive anomalous dimension. This brings the gravitons of QEG on a par with arbitrary (standard model, etc.) particles which exist as asymptotic states. We also argue that metric perturbations on almost Planckian scales might not be propagating, and we propose an interpretation as a form of `dark matter'.
Highlights
Anomalous dimension in single- and bi-metric truncationsOur approach to the quantization of gravity assumes that the fundamental degrees of freedom mediating the gravitational interaction are carried by the spacetime metric
Within the Asymptotic Safety scenario, we discuss whether Quantum Einstein Gravity (QEG) can give rise to a semi-classical regime of propagating physical gravitons governed by an effective theory which complies with the standard rules of local quantum field theory
We show that the problem disappears using the bi-metric renormalization group flows that became available recently: they admit an asymptotically safe UV limit and, at the same time, a genuine semi-classical regime with a positive anomalous dimension
Summary
Our approach to the quantization of gravity assumes that the fundamental degrees of freedom mediating the gravitational interaction are carried by the spacetime metric It heavily relies upon the Effective Average Action (EAA), a k-dependent functional Γk gμν, gμν, ξμ, ξμ which, in the case of QEG, depends on the dynamical metric gμν, the background metric gμν, and the diffeomorphism ghost ξμ and anti-ghost ξμ, respectively. 1 2 ddx√ghμν Γgkrav (2)[g, g] hρσ + O h3 This expansion in powers of hμν is referred to as the ‘level representation’ of the EAA, and a term is said to belong to level-(p) if it contains p factors of hμν, for p = 0, 1, 2, · · ·. The level-(p) couplings G(kp), Λ(kp), by definition, correspond to invariants that are of order (hμν)p Their relation to the ‘Dyn’ and ‘B’ couplings that were used in eq (2.3) is given by, for p = 0,
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